Coat bottoms of 2 (9-inch) round cake pans with cooking spray (do not coat sides of pans); line bottoms with wax paper. Coat wax paper with cooking spray; dust with 1 tablespoon flour.
Place granulated sugar, butter, and vanilla in a large bowl; beat with a mixer at medium speed until well blended (about 5 minutes). Add eggs, 1 at a time, beating well after each addition. Lightly spoon 2 1/4 cups flour into dry measuring cups; level with a knife. Combine 2 1/4 cups flour and next 4 ingredients (2 1/4 cups flour through nutmeg), stirring well with a whisk. Add flour mixture and milk alternately to sugar mixture, beginning and ending with flour mixture.
Pour batter into prepared pans; sharply tap pans once on counter to remove air bubbles. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on a wire rack; remove from pans. Cool completely on wire rack.
Place jam in a small bowl, and stir with a whisk until smooth. Place 1 cake layer on a plate; spread with 1/2 cup jam. Top with other cake layer; spread remaining jam over top of cake. Sprinkle with powdered sugar.