1. Melt butter in large skillet. Add onions and cook over medium heat just until onions are tender but not browned.
2. Blend in soup and milk and heat to boiling. Reduce heat to low.
3. Carefully break eggs into a saucer, then slide into sauce, one by one, side by side.
4. Cover skillet and cook 7 to 10 minutes or until eggs are cooked to taste.
5. While eggs are cooking, toast muffins and butter.
6. Place a muffin half on a plate, top with 1 slice of ham. Cover with 1 egg and some of the sauce.