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.