As others have recommended in comments, it looks like the canonical way to test Express controllers is through supertest.

An example test might look like this:

describe('GET /users', function(){
  it('respond with json', function(done){
    request(app)
      .get('/users')
      .set('Accept', 'application/json')
      .expect(200)
      .end(function(err, res){
        if (err) return done(err);
        done()
      });
  })
});

Upside: you can test your entire stack in one go.

Downside: it feels and acts a bit like integration testing.