Makes 20 fritters; serves 6
Melt butter in a 12-inch skillet over medium-high heat. Add apples and saute, stirring frequently, for 2 minutes. Sprinkle in brown sugar, 1/4 teaspoon cinnamon, nutmeg, and salt and continue to cook 2 to 3 minutes longer, or until apples are lightly coated with syrup. Remove pan from heat and set aside to cool.
In a small bowl, whisk together egg yolks and apple cider. Stir in the cooled apple mixture.
In a medium bowl, combine flour, baking powder, and 1 tablespoon sugar. Make a well in the center of the flour and add apple mixture. Gradually incorporate flour into wet ingredients, mixing gently with a whisk until uniform. Set batter aside for 20 minutes.
Fit a hand mixer with the whisk attachments and beat egg whites until soft peaks form. Gently fold whites into batter until completely blended.
In a medium bowl, combine remaining 1/2 cup sugar with remaining 1 teaspoon cinnamon.
Add enough oil to a heavy-bottomed Dutch oven or a deep cast iron skillet to come 4 inches up sides of pan. Heat oil over medium-high heat to 350 degrees. When oil is hot, carefully add 2-tablespoon scoops of batter, working in batches and being careful not to overcrowd pan. Maintain oil's heat between 300 and 350 degrees by adjusting burner as necessary. Fry fritters 4 to 5 minutes until golden and cooked through, turning them as needed for even color. Remove fritters with a slotted spoon or strainer, drain briefly, then toss them in cinnamon sugar. Transfer fritters to a serving platter. Repeat with remaining batter. Right before serving, roll fritters a final time in cinnamon sugar.