Melt 2 tablespoons butter in a saucepan. Add mushrooms, onion, green pepper, and garlic. Saute until vegetables are tender. Stir in tomatoes, water, bay leaf and cayenne. Bring to a boil; reduce heat and simmer 30 minutes, stirring occasionally.
Combine eggs, milk and salt and pepper to taste. Mix until eggs are lemony and frothy.
Melt 2 tablespoons butter in a large skillet over medium low heat. Pour in half the egg mixture and cook until bottom is set. Gently lift and allow uncooked egg to flow underneath.
Repeat with remaining egg being sure milk and butter are hot before adding egg mixture.