How to programatically add new menu items to menu item in PyGObject.

app.py

"""
Hierarchy is:
- GtkMenuBar
 - GtkMenuItem
  - GtkMenu
   - GtkMenuItem
   - GtkImageMenuItem
   - GtkCheckMenuItem
   - GtkRadioMenuItem
   - GtkSeparatorMenuItem
"""

from gi.repository import Gtk
from os.path import abspath, dirname, join

WHERE_AM_I = abspath(dirname(__file__))


class MyApp(object):

    def __init__(self):
        """
        Build GUI
        """
        # States
        self.counter = 0

        # Build GUI from Glade file
        self.builder = Gtk.Builder()
        self.glade_file = join(WHERE_AM_I, 'ui.glade')
        self.builder.add_from_file(self.glade_file)

        # Get objects
        go = self.builder.get_object
        self.window = go('window')
        self.menubar = go('menubar')

        # Connect signals
        self.builder.connect_signals(self)

        # Configure interface
        self.window.connect('delete-event', lambda x, y: Gtk.main_quit())

        # Everything is ready
        self.window.show()

    def populate_menu(self, num):
        """
        Populate application menu
        """
        content = [
            'Path to file 1',
            'Path to file 2',
            'Path to file 3',
            'Path to file 4',
        ]

        # Create menu
        menu = Gtk.MenuItem(label='My Menu {}'.format(num))
        menu.set_submenu(Gtk.Menu())

        for p in content:
            menu.get_submenu().append(Gtk.MenuItem(label=p))

        self.menubar.append(menu)
        menu.show_all()

    def _btn_cb(self, widget, data=None):
        """
        Button callback
        """
        self.populate_menu(self.counter)
        self.counter += 1
        print('Created menu #{}'.format(self.counter))

if __name__ == '__main__':
    gui = MyApp()
    Gtk.main()

ui.glade

<?xml version="1.0" encoding="UTF-8"?>
<interface>
  <!-- interface-requires gtk+ 3.0 -->
  <object class="GtkWindow" id="window">
    <property name="can_focus">False</property>
    <child>
      <object class="GtkBox" id="box">
        <property name="visible">True</property>
        <property name="can_focus">False</property>
        <property name="orientation">vertical</property>
        <child>
          <object class="GtkMenuBar" id="menubar">
            <property name="height_request">20</property>
            <property name="visible">True</property>
            <property name="can_focus">False</property>
          </object>
          <packing>
            <property name="expand">False</property>
            <property name="fill">True</property>
            <property name="position">0</property>
          </packing>
        </child>
        <child>
          <object class="GtkButton" id="button">
            <property name="label" translatable="yes">Click Me</property>
            <property name="visible">True</property>
            <property name="can_focus">False</property>
            <property name="receives_default">True</property>
            <signal name="clicked" handler="_btn_cb" swapped="no"/>
          </object>
          <packing>
            <property name="expand">True</property>
            <property name="fill">True</property>
            <property name="position">1</property>
          </packing>
        </child>
      </object>
    </child>
  </object>
</interface>