New Twiddle

components.my-button.js

import Ember from 'ember';

export default Ember.Component.extend({
  tagName: 'button',
  click() {
    this.sendAction();
  }
});

components.my-component.js

import Ember from 'ember';

export default Ember.Component.extend({
});

components.my-fourth.js

import Ember from 'ember';

export default Ember.Component.extend({
});

components.my-mid.js

import Ember from 'ember';

export default Ember.Component.extend({
});

components.my-third.js

import Ember from 'ember';

export default Ember.Component.extend({
});

controllers.application.js

import Ember from 'ember';

export default Ember.Controller.extend({
  appName: 'Ember Twiddle',
    actions: {
    	theAction() {
      	alert('the highest action');
    	}
  }
});

templates.application.hbs

{{#my-component theAction=(action 'theAction')}}
	{{#my-mid}}
    {{#my-third}}
      {{#my-fourth}}
        <button onclick={{action "theAction"}}>clickMe</button>
       {{/my-fourth}}
    {{/my-third}}
  {{/my-mid}}
{{/my-component}}

templates.components.my-button.hbs

{{yield}}

templates.components.my-component.hbs

{{yield (action 'parentAction')}}

templates.components.my-fourth.hbs

and 4th
{{yield}}

templates.components.my-mid.hbs

{{yield (action 'parentAction')}}

templates.components.my-third.hbs

and ... 3rd
{{yield}}

twiddle.json

{
  "version": "0.10.4",
  "EmberENV": {
    "FEATURES": {}
  },
  "options": {
    "use_pods": false,
    "enable-testing": false
  },
  "dependencies": {
    "jquery": "https://cdnjs.cloudflare.com/ajax/libs/jquery/1.11.3/jquery.js",
    "ember": "2.7.0",
    "ember-data": "2.7.0",
    "ember-template-compiler": "2.7.0"
  },
  "addons": {}
}