1. Peel the apples and place them in a large bowl of water. Squeeze the juice from the lemon into the water to prevent the apples from browning.
2. One at a time, cut the apples in half and remove the core. Place each half down on a cutting board and cut into 1/8″ slices.
3. Combine the sugars, cinnamon and nutmeg together and toss with the apple slices. Allow the apple slices to sit for at least 30 minutes in the mixture to release their juices.
4. Preheat the oven to 375 F and line a pie dish with the pie crust, and prick the bottom of the crust with a fork.
5. Drain the apples, reserving the juice for later. Starting on the outside edge of the pie crust, begin placing the apple slices, one at a time around the pie dish, overlapping the slices and working in a large circle towards the center of the dish. Pack the slices in tightly, filling in any gaps with remaining apple splices. Roll up one apple slice to create the center “bud” shape. Pour half of the reserved liquid over the pie. Cover with foil, and bake for 40 minutes. Remove the foil and bake for an additional 15-20 minutes, or until golden brown.
6. While the pie cools, place the remaining reserved juice in a saucepan over medium heat, along with 1 tbsp butter. Bring the juice to a boil and allow it to cook for 10-15 minutes or until it has slightly reduced and thickened. Add the heavy cream and a pinch of salt (to taste) and stir well.
7. Serve the pie immediately, pouring the caramel sauce over the entire pie or each slice individually.

Leftover pie can be stored in an airtight container, in the fridge, for 3-4 days.