Preheat the oven to 350 degrees F (175 degrees C). Grease a 10-inch angel food cake pan and sprinkle with 1 tablespoon gluten-free flour.
Combine sugar and mascarpone cheese in the bowl of a stand mixer. Beat on medium speed, scraping bowl often, until creamy. Add eggs 1 at a time, beating well after each addition. Add vanilla extract and beat until well mixed.
Stir 3 cups gluten-free flour and baking powder together in a bowl. Reduce mixer speed to low. Gradually add flour mixture to egg mixture alternately with milk until well blended. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 50 to 60 minutes. Cool for 10 minutes in the pan before inverting onto a cooling rack.
