Larger button menu?

Is it possible to create a menu button where the entire button acts as the drop down instead of just the downward arrow next to the button? In some cases, i'd rather click on a larger target (the button's image and it's label) instead of the smaller arrow.

Create a new Menu item instead of a new Menu Button item.

Just for what it's worth, there's also a known bug in the menu button that limits the clickable focus for the actual submenu to the lower half of the down arrow part of the button when the button label is to either side of the icon.