Preheat oven to 300 degrees F.
Mix together ground beef, 3/4 cup cheese, ground flaxseed, 1/3 cup milk, onion, and egg. Shape into small meatballs.
Combine flour, pepper, and salt. Put alternate layers of potatoes and beans in baking dish. Sprinkle flour mixture and remaining cheese over top. Mix soup and 1 cup milk and pour over vegetables. Top with meatballs.
Bake for 2 hours or until done.