In small bowl, beat 3/4 cup of the cooking sauce (reserve remaining sauce) and eggs with whisk or fork until well mixed. Pour into shallow bowl or pie plate.
In 12-inch nonstick skillet, melt 1 tablespoon of the butter over medium heat. Carefully dip 3 slices bread, one at a time, into sauce mixture. Allow excess to drip off. Place 3 slices in skillet; sprinkle each with 1/4 cup cheese. Place top slices of bread over cheese to make 3 sandwiches.
Cook uncovered over medium heat 3 to 4 minutes or until bottoms are golden brown. Turn and cook 3 to 4 minutes longer or until bottoms are golden brown and cheese is melted. Repeat with remaining butter, bread, sauce mixture and cheese. Heat reserved sauce until hot; serve with sandwiches as dipping sauce.