How To Disable The GNOME Shell AppMenu While Retaining Its Functionality

GNOME has introduced the AppMenu for some of its core applications a while back (for some applications like Epiphany, with GNOME 3.4 and for others like Nautilus, etc. with GNOME 3.6), meaning that part of the menu or the whole menu is displayed as a drop-down on the top GNOME Shell bar.
While using an AppMenu for actions that affect the entire application and another one for window-specific actions makes sense in theory, in reality this seems to have caused confusion, inconsistency and some would say that it brings no real benefit. Further more, GNOME Shell's top bar is only displayed on the main monitor when using multiple monitors and thus, if you want to access it for an application that's displayed on another monitor, the mouse needs to travel a considerable distance.
So here's how to remove the AppMenu, but retain its functionality.