1Heat 12-inch nonstick skillet over medium heat. Divide sausage in half and shape into flat patties slightly bigger than the diameter of each bread slice. Place patties in hot skillet and cook about 8 minutes, turning once, until pork is no longer pink in center. Drain on paper towel-lined plate. Drain fat from skillet and wipe out with a wadded paper towel.
2In same skillet, heat oil over medium heat until hot. Break each egg into skillet and sprinkle with salt and pepper if desired. Cook until whites of eggs are set. Flip eggs so yolks face down (flip eggs away from you to avoid being splashed with hot oil). Use tip of spatula to pierce each yolk. Cook eggs 1 minute or until yolks are set. Remove eggs from skillet and place directly on top of sausage patties on paper towels.
3Spread 2 tablespoons apple butter on one side of 2 bread slices. Top each slice with sausage and egg. Sprinkle each with 1/4 cup cheese. Cover with remaining bread slices. Spread half of the butter over the top slices of bread.
4In same skillet, place sandwiches butter sides down. Spread remaining butter over top slices of bread. Cook uncovered over medium heat about 5 minutes or until bottoms are golden brown. With spatula, carefully turn sandwiches over. Cook 2 to 3 minutes longer or until bottoms are golden brown and cheese is melted. Serve hot.