Preheat the oven to 350 degrees F (175 degrees C).
Cover the bottom of a 10x15-inch baking pan with brown sugar and 2 tablespoons cinnamon. Layer apple slices on top.
Place flour, apple juice, white sugar, butter, eggs, milk, remaining 1 tablespoon cinnamon, vanilla extract, baking powder, and salt in the bowl of a stand mixer fitted with the paddle attachment. Mix until completely smooth, 5 to 10 minutes; the longer you mix, the fluffier the cake will be.
Pour batter over apples in the baking pan, making sure they are evenly covered.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, 45 to 55 minutes. Cool for 20 to 30 minutes. Place a large serving dish over the cake and carefully flip over.