Preheat broiler. Melt butter in a 10-inch ovenproof skillet over medium-high heat. Add sliced turkey bacon, cook about 3 minutes. Pour in eggs, season with salt and pepper, cook until almost set but still runny on top, about 2 minutes.

Sprinkle cheese over eggs and broil until cheese is melted and browned, 3 to 4 minutes. Slide the frittata onto a serving platter and cut into wedges.

Serve with small dishes of applesauce.