Place a rack in the center of the oven and preheat the oven to 350 degrees F. Generously grease two 9-inch round cake pans with solid vegetable shortening, then dust with flour. Shake out the excess flour. Set the pans aside.
Place the cake mix, milk, melted butter, eggs, and vanilla extract in a large mixing bowl. Blend with an electric mixer on low speed for 1 minutes. Stop the machine and scrape down the sides of the bowl with a rubber spatula. Increase the mixer speed to medium and beat 2 minutes more, scraping the sides down again if needed. The batter should look well blended. Divide the batter between the prepared pans, smoothing it out with the rubber spatula. Place the pans in the oven side by side.
Bake the cakes until they are golden brown and spring back when lightly pressed with your finger, 27 to 29 minutes. Remove the pans from the oven and place them on wire racks to cool for 10 minutes. Run a dinner knife around the edge of each layer and invert each onto a rack, then invert them again onto another rack to that the cakes are right side up. Allow them to cool completely, 30 minutes more.
Meanwhile, prepare the Quick Caramel Frosting.
Place one cake layer, right side up, on a serving platter. Spread the top with the warm frosting. Place the second layer, right side up, on top of the first layer and frost the top and sides of the cake with clean, smooth strokes. Work quickly, as the frosting will set. (If the frosting gets too hard to work with, place the pan back over low heat for 1 minute, stirring constantly, to soften it up.) Once the frosting has set, slice and serve.
Store this cake, covered in plastic wrap or aluminum foil, at room temperature for up to 1 week or freeze, wrapped in foil, for up to 6 months. Thaw the cake overnight on the counter before serving.
Place the butter and brown sugars in a medium-size heavy saucepan over medium heat. Stir and cook until the mixture comes to a boil, about 2 minutes. Add the milk, stir, and bring the mixture back to a boil, then remove the pan from the heat. Add the confectioners' sugar and vanilla. Beat with a wooden spoon until the frosting is smooth.
Use immediately (while still warm) to frost the cake of your choice or the frosting will harden. If it does harden while you are frosting the cake, simply place the pan back over low heat and stir until the frosting softens up.
Recipe courtesy of Ann Byrn, author, "The Cake Mix Doctor" (Workman, 2000)