Preheat the oven to 375 degrees F (190 degrees C). Coat a 9-inch deep-dish pie plate with cooking spray.
Mix together sugar and butter in a large bowl until smooth. Add egg yolks and beat until light and fluffy. Sift in cake flour, baking powder, and salt; stir until well-blended. Mix in milk and vanilla until combined.
Whip egg whites with an electric mixer in a separate bowl to stiff peaks. Fold into batter. Pour into the prepared pie plate; sprinkle cinnamon sugar on top.
Bake in the preheated oven for 25 minutes, then reduce temperature to 325 degrees F (165 degrees C). Continue baking until the center is set when pie is gently jiggled, 25 to 30 minutes.