How to properly break out of a promise chain?

Firstly, I think it better to say you are seeking to "bypass" (part of) the promise chain rather than to "break" it.

As you say, testing for "emptyResult" in several places is pretty ugly. Fortunately, a more elegant mechanism is available while adhering to the same general principle of not executing some of the promise chain.

An alternative mechanism is to use promise rejection to control the flow, then to re-detect the specific error condition(s) later in the chain, and put it back on the success path.

Menus.getCantinas().then(function(cantinas) {
    Menus.cantinas = cantinas;
    if(cantinas.length == 0) {
        return $.Deferred().reject(errMessages.noCantinas);
    } else {
        return $.when(Menus.getMeals(cantinas), Menus.getSides(cantinas));
    }
}).then(function(meals, sides) {
    Menus.sides = sides;
    Menus.meals = meals;
    return Menus.getAdditives(meals, sides);
}).then(function(additives) {
    Menus.additives = additives;
    return Menus;
}).then(null, function(err) {
    //This "catch" exists solely to detect the noCantinas condition 
    //and put the chain back on the success path.
    //Any genuine error will be propagated as such.
    //Note: you will probably want a bit of safety here as err may not be passed and may not be a string.
    return (err == errMessages.noCantinas) ? $.when(Menus) : err;
}).done(function(Menus) {
    // with no cantinas, or with everything
});

var errMessages = {
    'noCantinas': 'no cantinas'
};

On the plus side, I find the lack of nesting makes for better readability of the natural success path. Also, for me at least, this pattern would require minimal mental juggling to accommodate further bypasses, if needed.

On the down side, this pattern is slightly less efficient than Bergi's. Whereas the main path has the same number of promises as Bergi's, the cantinas.length == 0 path requires one more (or one per bypass if multiple bypasses were coded). Also, this pattern requires reliable re-detection of specific error condition(s) - hence the errMessages object - which some may find detracts.

For folks using built-in browser promises and looking for a way to halt the promise chain without making all consumers know about the rejection case, triggering any chained then's or catches or throwing any Uncaught (in promise) errors, you can use the following:

var noopPromise = {
  then: () => noopPromise, 
  catch: () => noopPromise
}

function haltPromiseChain(promise) {
  promise.catch(noop)

  return noopPromise
}

// Use it thus:
var p = Promise.reject("some error")
p = haltPromiseChain(p)
p.catch(e => console.log(e)) // this never happens

Basically, noopPromise is a basic stubbed out promise interface that takes chaining functions, but never executes any. This relies on the fact that apparently the browser uses duck-typing to determine if something is a promise, so YMMV (I tested this in Chrome 57.0.2987.98), but if that becomes a problem you could probably create an actual promise instance and neuter its then and catch methods.

Sounds like you want to branch, not to break - you want to continue as usual to the done. A nice property of promises is that they don't only chain, but also can be nested and unnested without restrictions. In your case, you can just put the part of the chain that you want to "break" away inside your if-statement:

Menus.getCantinas().then(function(cantinas) {
    Menus.cantinas = cantinas;

    if (cantinas.length == 0)
        return Menus; // break!

    // else
    return $.when(Menus.getMeals(cantinas), Menus.getSides(cantinas))
    .then(function(meals, sides) {
        Menus.sides = sides;
        Menus.meals = meals;
        return Menus.getAdditives(meals, sides);
    }).then(function(additives) {
        Menus.additives = additives;
        return Menus;
    });
}).done(function(Menus) {
    // with no cantinas, or with everything
});