The local sub shop here carves out the middle of the bread so the meatballs are cradled nicely in a pocket. They add cheese slices on the bottom so the sauce don't saturate the bread. Still messy but better.

Bread causes me distress. Atkins has a all meat meatball recipe that works nicely without wheat.

So it binds together and gets the true meatball texture with nary a breadcrumb? What does it use? I'm imagining anything from egg to cornstarch.