Mix 1/4 teaspoon salt and 1/4 cup onions in the ground beef. Pat meat by hand or in hamburger press to 3/4 inch thickness. Set aside. In bowl, mix bread cubes with chopped onion, celery, salt, and pepper. Beat eggs, 1/4 cup milk, and 1/2 cup of soup together. Combine liquid mixture with bread cubes. Grease a large shallow baking dish. Put several rounded tablespoons of bread cube mixture into center of beef patties. Turn edges of ground beef patties up. Bake 30 minutes at 350 degrees. Mix rest of milk with rest of mushroom soup. Pour over hamburgers and stuffing. Bake for 25 more minutes. Serve with whipped potatoes and salad.