To prepare the filling, melt 2 tablespoons butter in a large, heavy saucepan over medium heat. Add 1/2 cup brown sugar and 1/4 cup evaporated milk, stirring constantly, and cook for 2 minutes. Bring to a boil, and cook for 30 seconds. Remove from heat. Heat 1 cup 2% milk in a small, heavy saucepan over medium-heat to 180° or until tiny bubbles form around the edge (do not boil). Remove milk from heat.
Combine the cornstarch, 1/8 teaspoon salt, 1 egg, and egg yolk in a bowl; stir well with a whisk. Gradually add hot 2% milk to egg mixture, stirring constantly. Add milk-egg mixture to brown sugar mixture, stirring constantly. Cook over medium heat until mixture comes to a boil, stirring constantly; cook 1 minute. Stir in 1 teaspoon vanilla. Spoon filling into a bowl. Cover surface of filling with plastic wrap; chill.
Preheat oven to 350°.
To prepare cake, coat bottom of a 9-inch round cake pan with cooking spray (do not coat sides of pan); line bottom with wax paper. Coat the wax paper with cooking spray, and dust with 2 teaspoons flour. Lightly spoon 1 1/4 cups flour into dry measuring cups, and level with a knife. Combine 1 1/4 cups flour, baking powder, and 1/4 teaspoon salt in a bowl. Place 1 tablespoon butter and 1/3 cup 2% milk in a small, heavy saucepan, and bring to a simmer over medium heat (do not boil). Remove from heat. Cover and keep warm.
Beat 2 eggs in a large bowl with a mixer at high speed for 3 minutes. Gradually add 1/3 cup brown sugar and granulated sugar, beating until thick (about 3 minutes). Add flour mixture to egg mixture alternately with warm milk mixture, beginning and ending with flour mixture. Stir in 1 teaspoon vanilla. Pour batter into prepared pan. Bake at 350° for 25 minutes or until a wooden pick inserted in center comes out clean. Cool cake in pan on a wire rack 10 minutes. Remove cake from pan; peel off wax paper. Cool cake completely on wire rack.
Split cake in half horizontally using a serrated knife; place bottom layer,