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1
Place a large skillet over medium-high heat and melt 1 tablespoon butter just until the edges of the butter look slightly browned and smells nutty, about 1 minute. Stir apples into butter and cook until they just begin to soften, about 2 minutes. Sprinkle with sugar and continue to cook until apples are soft and slightly caramelized, about 5 minutes. Transfer apples to a plate and spread out to cool.
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2
Preheat oven to 400 degrees F (200 degrees C). Grease 4 ramekins generously with butter. Place ramekins onto a sheet pan.
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3
Melt 2 tablespoons butter in a small skillet over medium heat; stir in flour and cook until mixture is smooth and raw taste of flour is cooked out of the roux, 2 to 3 minutes. Pour milk into roux, bring to a simmer, and whisk until mixture thickens to a smooth white sauce, about 2 minutes. Cook, whisking, for 1 minute more and remove from heat; cool white sauce to lukewarm temperature.
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4
Pour white sauce into a large mixing bowl and whisk in salt, black pepper, cayenne pepper, nutmeg, and egg yolks. Stir Cheddar cheese into white sauce mixture until thoroughly combined.
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5
Whisk egg whites in a glass or metal bowl until they hold soft, fluffy peaks, about 2 minutes. Gently fold half the beaten egg whites into the souffle batter. Repeat with remaining whites to make a soft, airy batter. Fold in cooled apple mixture. Divide mixture into prepared ramekins.
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6
Bake in the preheated oven until souffles have risen and tops are browned, about 22 minutes. Souffles will fall slightly as they cool. Serve warm.
