Preheat oven to 350°.
To prepare cake, coat 2 (8-inch) round cake pans with cooking spray; line bottoms of pans with wax paper. Lightly coat wax paper with cooking spray; dust pans with 1 tablespoon flour. Set aside.
Place 1 cup light brown sugar and 7 tablespoons butter in a large mixing bowl; beat with a mixer at medium speed 3 minutes or until well blended. Add egg substitute to sugar mixture; beat well. Lightly spoon 2 cups flour into dry measuring cups; level with a knife. Combine flour, baking powder, baking soda, and 1/4 teaspoon salt, stirring well with a whisk. Add flour mixture to sugar mixture alternately with 1 cup milk, beginning and ending with flour mixture.
Spoon 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. Remove wax paper; discard. Cool cakes completely on wire rack.
To prepare frosting, combine 1/2 cup dark brown sugar and remaining ingredients in a medium, heavy saucepan over medium heat; bring to a boil. Cook 2 minutes or until mixture is thick, stirring constantly.
Place 1 cake layer on a plate; spread with 1/3 cup frosting. Top with remaining cake layer. Spread remaining frosting over top and sides of cake.
Work quickly to spread the frosting on the cake before it begins to set. We call for light brown sugar in the cake to lend a subtly sweet flavor, but dark brown in the frosting to provide a contrasting rich caramel flavor. You can use light brown sugar for both the cake and frosting, if you prefer.