Coat 3 (8-inch) round cake pans with cooking spray; dust with 1 tablespoon flour.
Beat granulated sugar, butter, oil, and vanilla at medium speed of a mixer for 1 1/2 minutes or until well-blended. Add brown sugar, yogurt, and egg whites; beat at high speed of a mixer 1 1/2 minutes.
Lightly spoon 3 cups sifted cake flour into dry measuring cups. Combine sifted flour and next 5 ingredients (flour through nutmeg) in a bowl. Add flour mixture to creamed mixture alternately with milk, beginning and ending with flour mixture.
Pour cake batter into prepared pans. Sharply tap pans once on counter to remove air bubbles. Bake at 350° for 24 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on wire racks; remove from pans. Cool completely on wire racks.
Place 1 cake layer on a plate. Spread with 1/3 cup Caramel Frosting; top with another cake layer. Spread with 1/3 cup frosting, and top with the remaining cake layer. Spread remaining frosting over top and sides of cake.