You should create a subclass of NSPopUpButtonCell, then override
- (void)drawBezelWithFrame:(NSRect)frame inView:(NSView *)controlView
NSPopupButtonCell is a subclass of NSButtonCell which defines several methods for drawing individual cell components, eg bezel, title, image.
You can then expand the NSPopupButton and change its cell subclass to your new subclass and it should use your drawing methods.
Cocoa primarily uses NSCell to handle drawing, unlike iOS