A slight modification on the example by Michał Perłakowski with the benefit of this approach being that the nested proxy is only created once rather than every time a value is accessed.

If the property of the proxy being accessed is an object or array, the value of the property is replaced with another proxy. The isProxy property in the getter is used to detect whether the currently accessed object is a proxy or not. You may want to change the name of isProxy to avoid naming collisions with properties of stored objects.

Note: the nested proxy is defined in the getter rather than the setter so it is only created if the data is actually used somewhere. This may or may not suit your use-case.

const handler = {
  get(target, key) {
    if (key == 'isProxy')
      return true;

    const prop = target[key];

    // return if property not found
    if (typeof prop == 'undefined')
      return;

    // set value as proxy if object
    if (!prop.isProxy && typeof prop === 'object')
      target[key] = new Proxy(prop, handler);

    return target[key];
  },
  set(target, key, value) {
    console.log('Setting', target, `.${key} to equal`, value);

    // todo : call callback

    target[key] = value;
    return true;
  }
};

const test = {
  string: "data",
  number: 231321,
  object: {
    string: "data",
    number: 32434
  },
  array: [
    1, 2, 3, 4, 5
  ],
};

const proxy = new Proxy(test, handler);

console.log(proxy);
console.log(proxy.string); // "data"

proxy.string = "Hello";

console.log(proxy.string); // "Hello"

console.log(proxy.object); // { "string": "data", "number": 32434 }

proxy.object.string = "World";

console.log(proxy.object.string); // "World"

I published a library on GitHub that does this as well. It will also report to a callback function what modifications have taken place along with their full path.

Michal's answer is good, but it creates a new Proxy every time a nested object is accessed. Depending on your usage, that could lead to a very large memory overhead.

I have also created a library type function for observing updates on deeply nested proxy objects (I created it for use as a one-way bound data model). Compared to Elliot's library it's slightly easier to understand at < 100 lines. Moreover, I think Elliot's worry about new Proxy objects being made is a premature optimisation, so I kept that feature to make it simpler to reason about the function of the code.

observable-model.js

let ObservableModel = (function () {
    /*
    * observableValidation: This is a validation handler for the observable model construct.
    * It allows objects to be created with deeply nested object hierarchies, each of which
    * is a proxy implementing the observable validator. It uses markers to track the path an update to the object takes
    *   <path> is an array of values representing the breadcrumb trail of object properties up until the final get/set action
    *   <rootTarget> the earliest property in this <path> which contained an observers array    *
    */
    let observableValidation = {
        get(target, prop) {
            this.updateMarkers(target, prop);
            if (target[prop] && typeof target[prop] === 'object') {
                target[prop] = new Proxy(target[prop], observableValidation);
                return new Proxy(target[prop], observableValidation);
            } else {
                return target[prop];
            }
        },
        set(target, prop, value) {
            this.updateMarkers(target, prop);
            // user is attempting to update an entire observable field
            // so maintain the observers array
            target[prop] = this.path.length === 1 && prop !== 'length'
                ? Object.assign(value, { observers: target[prop].observers })
                : value;
            // don't send events on observer changes / magic length changes
            if(!this.path.includes('observers') && prop !== 'length') {
                this.rootTarget.observers.forEach(o => o.onEvent(this.path, value));
            }
            // reset the markers
            this.rootTarget = undefined;
            this.path.length = 0;
            return true;
        },
        updateMarkers(target, prop) {
            this.path.push(prop);
            this.rootTarget = this.path.length === 1 && prop !== 'length'
                ? target[prop]
                : target;
        },
        path: [],
        set rootTarget(target) {
            if(typeof target === 'undefined') {
                this._rootTarget = undefined;
            }
            else if(!this._rootTarget && target.hasOwnProperty('observers')) {
                this._rootTarget = Object.assign({}, target);
            }
        },
        get rootTarget() {
            return this._rootTarget;
        }
    };

    /*
    * create: Creates an object with keys governed by the fields array
    * The value at each key is an object with an observers array
    */
    function create(fields) {
        let observableModel = {};
        fields.forEach(f => observableModel[f] = { observers: [] });
        return new Proxy(observableModel, observableValidation);
    }

    return {create: create};
})();

It's then trivial to create an observable model and register observers:

app.js

// give the create function a list of fields to convert into observables
let model = ObservableModel.create([
    'profile',
    'availableGames'
]);

// define the observer handler. it must have an onEvent function
// to handle events sent by the model
let profileObserver = {
    onEvent(field, newValue) {
        console.log(
            'handling profile event: \n\tfield: %s\n\tnewValue: %s',
            JSON.stringify(field),
            JSON.stringify(newValue));
    }
};

// register the observer on the profile field of the model
model.profile.observers.push(profileObserver);

// make a change to profile - the observer prints:
// handling profile event:
//        field: ["profile"]
//        newValue: {"name":{"first":"foo","last":"bar"},"observers":[{}
// ]}
model.profile = {name: {first: 'foo', last: 'bar'}};

// make a change to available games - no listeners are registered, so all
// it does is change the model, nothing else
model.availableGames['1234'] = {players: []};

Hope this is useful!

I wrote a function based on Michał Perłakowski code. I added access to the path of property in the set/get functions. Also, I added types.

    const createHander = <T>(path: string[] = []) => ({
        get: (target: T, key: keyof T): any => {
            if (key == 'isProxy') return true;
            if (typeof target[key] === 'object' && target[key] != null)
                return new Proxy(
                    target[key],
                    createHander<any>([...path, key as string])
                );
            return target[key];
        },
        set: (target: T, key: keyof T, value: any) =>  {
            console.log(`Setting ${[...path, key]} to: `, value);
            target[key] = value;
            return true;
        }
    });
    
    const proxy = new Proxy(obj ,createHander<ObjectType>());