Add a lightly beaten egg, but not too much. The egg acts as a binder for the ingredients, but only a small amount is needed. A small egg will do for a pound of minced meat. Alternatively, if you follow an egg-free diet, you can soak fresh bread in milk, squeezing out excess milk, to use as a binder.
The only way to keep the meatballs from falling apart is to add some flour to the pre-cooked and seasoned ground beef. Once you season the ground beef to your liking, add a little flour, not too much, but at least half a handful. Then mix all the ground beef and flour very well, then start frying them in the pan and they will remain intact. Arguably, veal meatballs are the most familiar to many people in the world, but meatballs are also made with pork, chicken, venison, or a mix of meats.
I also try to put the meatballs in the hot oil and immediately stir them gently to cover the outside of all the meatballs with oil, since I think this helps prevent them from sticking to the pan, which can cause them to break when I try to turn them over.