Using whisk, gently stir until just blended. Add flour mixture. Pour batter into prepared pan. Bake cake until tester inserted into center comes out clean, about 20 minutes. Line cake rack with paper towels.
Dust towels generously with powdered sugar.
Peel off parchment. Cool cake completely. Repeat 2 more times, using same amount of each ingredient to make 2 more cake layers. Place in freezer until filling is firm, about 15 minutes. Spread with remaining filling.