Mix beef, eggs, saltines, and onion soup mix together. Form into medium-sized meatballs.
Melt butter in a frying pan over medium-low heat. Add meatballs; cover and cook, turning frequently, until evenly browned, 8 to 10 minutes.
Pour cream of mushroom soup into a bowl. Fill empty can 3/4 full with milk and mix into the soup. Pour sauce over meatballs and simmer until thickened, about 10 minutes more.