Coat bottoms of 2 (9-inch) round cake pans with cooking spray (do not coat sides of pan), and line bottoms of pans with wax paper. Coat wax paper with cooking spray, and dust with 1 tablespoon flour.
Combine water and oats in a medium bowl; let stand 20 minutes. Beat granulated sugar, brown sugar, shortening, and vanilla at medium speed of a mixer for 5 minutes. Add eggs, 1 at a time, beating well after each addition. Add oatmeal, beating until blended.
Lightly spoon 1 1/2 cups flour into dry measuring cups; level with a knife. Combine 1 1/2 cups flour, baking soda, cinnamon, salt, and nutmeg, stirring well with a whisk. Add flour mixture to sugar mixture alternately with buttermilk, 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 35 minutes or until a wooden pick inserted in center comes out clean. Cool in pans 10 minutes on a wire rack; remove from pans. Remove wax paper. Cool completely on wire rack.
Place 1 cake layer on a plate; spread layer with 1/2 cup Caramel-Pecan Frosting, and top with the remaining layer. Spread the remaining frosting over the top and sides of cake. Store the cake loosely covered in refrigerator.