Preheat oven to 350°.
To prepare cake, coat bottoms of 2 (9-inch) round cake pans with cooking spray (do not coat sides of pans). Line bottoms of pans with wax paper. Coat wax paper with cooking spray, and dust with 2 teaspoons flour; set aside.
Place 1/3 cup butter in a large bowl; beat with a mixer at medium speed until creamy. Gradually add granulated sugar, beating well. Add egg yolks, one at a time, beating well after each addition.
Lightly spoon 2 cups flour into dry measuring cups; level with a knife. Combine 2 cups flour, baking soda, and salt; stir well. Add flour mixture and buttermilk alternately to butter mixture, beginning and ending with flour mixture. Stir in pecans, coconut extract, and 1 teaspoon vanilla.
Beat egg whites with a mixer at high speed until stiff peaks form (do not overbeat). Fold egg whites into batter; pour batter into prepared pans. Bake at 350° for 23 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 5 minutes on a wire rack. Loosen cake layers from sides of pans; remove from pans. Remove and discard wax paper. Cool completely.
To prepare frosting, place 1 tablespoon butter and cream cheese in a large bowl; beat with a mixer at high speed until fluffy. Gradually add powdered sugar, beating at low speed until smooth (do not overbeat). Add 1 teaspoon vanilla; beat well.
Place 1 cake layer on a plate; spread with one-third of frosting. Top with other cake layer. Spread remaining frosting over top and sides of cake.