Prep. Preheat the oven to 350℉ with the rack in the center.
Make the cake batter. Stir together the flour, salt, baking soda, baking powder, and spices in a large mixing bowl. Add both sugars, eggs, vegetable oil, and apple sauce and beat with a hand mixer until smooth, scraping down the sides of the bowl with a spatula if needed. Add the chopped apples and stir by hand,
Bake. Pour the batter into a 13x9 baking dish. Sart checking at 35 minutes for doneness. The cake is ready when it's golden brown and a toothpick inserted into the center comes out with just a few moist crumbs.
Cool. Cool in the pan for at least 2 hours before making the frosting.
Make the caramel frosting. Bring the brown sugar, butter, and milk to a boil in a 2-quart saucepan over medium heat, whisking constantly. Boil for 1 minute, continuing to whisk. Remove from the heat, and using a hand mixer, gradually beat in the powdered sugar until smooth and slightly thickened. Pour immediately over the cooled cake.
Cool and serve. Let the frosting cool and harden for at least 20 minutes. It should set up very quickly to form a firm layer. Cut into squares and serve.