Pour about 3/4 inch oil in a 12-inch skillet and heat 325 degrees F (165 degrees C).
Combine confectioners' sugar and 1/4 teaspoon cinnamon in a bowl. Mix flour, apple cider, egg, baking powder, vanilla extract, 1/2 teaspoon cinnamon, and salt together in a separate large bowl until batter is smooth. Pour batter into a funnel with a narrow spout or squeeze bottle, covering the opening with a clean finger.
Dispense batter into the hot oil in a spiral pattern, making about a 6-inch cake; cook until lightly browned, about 5 minutes per side. Transfer cake to a paper towel-lined plate and sprinkle confectioners' sugar mixture over cake.