Preheat the oven to 350° with the rack in the center.
Make the cake batter. Stir together flour, spices, salt, baking soda, baking powder, and spices in a large mixing bowl. Add the sugar, 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 chopped apples and stir by hand,
Bake. Pour batter into a 10 x 15-inch jelly roll pan or a 13 x 9 baking dish. Bake for 18-22 minutes, until the cake is golden brown and a toothpick inserted into the center comes out with just a few moist crumbs. Cool in the pan for at least 2 hours before making the frosting.
Cool. Cool in the pan for at least 2 hours before making the frosting.
Make the caramel frosting. Bring ½ cup brown sugar, ¼ cup butter, and 3 tablespoons of 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 powdered sugar until smooth, until the icing begins to cool and thickens slightly. 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.