About 8 cups vegetable oil, divided
2 Golden Delicious apples
1 ¾ cups self-rising cake flour, divided
1 large egg
3/4 cup sparkling apple cider
Confectioners’ sugar for dusting
1 inch round cookie cutter or a melon-ball cutter
Preheat oven to 250 F with rack in the middle. Set a cooling rack in a large shallow baking pan. Heat 2 inches oil in a 5 to 6 qt. heavy pot over medium-high heat to 375 F.Meanwhile, peel apples and cut crosswise into ¼ inch-thick slices. Cut out core with cutter, then pat apple rings dry. Put 1 ¼ cups flour in a large shallow bowl and make a well in the center. Beat egg in a small bowl with a fork, then stir cider and 1 tablespoon oil and pour into well. Stir with fork until lumpy batter forms. Working in batches of 3 or 4, dredge apple rings in remaining ½ cup flour, shaking off excess, then dip in batter to coat, letting excess drip off, and fry, gently turning over once with a slotted spoon, until golden brown on both sides, about 2 minutes total per batch. Transfer to rack and keep warm in oven. Return oil 372 F between batches. Just before serving, dust warm beignets with confectioners’ sugar.