1. Preheat the oven to 350 F. Butter and flour a 10-inch spring loaded cake pan. 
2. In a medium bowl, whisk together the flour, baking powder, baking soda, salt and spices. In the bowl of a mixer, cream together the butter, brown sugar and white sugar until combined. Beat in the eggs one at a time. Add the vanilla. Beat on medium-high speed until the mixture increases in volume and lightens in colour, about 3 to 4 minutes. 
3. With the mixer on low, alternate adding a third of the flour mixture followed by half of the milk to the batter. Stir until barely combined, then repeat with another third of the flour and the remaining milk. Add the final third of the flour mixture and stir until just combined. Scrape the batter into the pan. 
4. Press the thinly sliced apple pieces into the batter so that their rounded edges peek out of the batter and their flat edges almost touch the bottom of the pan. Arrange them in ever-smaller circles from the outside to the centre of the pan. Tuck any extra pieces closer to the edges of the pan where the cake bakes more quickly. Bake for 55 minutes.
5. Serve with Caramel Sauce