Preheat oven to 350°F (175°C). Wrap the outside bottom of the springform pan tightly with two layers of heavy-duty aluminum foil.

In a bowl, mix the graham cracker crumbs, brown sugar, and cinnamon. Pour in the melted butter and stir until the mixture resembles wet sand.

Press the crumb mixture firmly into the bottom and 1 inch up the sides of the prepared springform pan.

Bake for 8–10 minutes. Remove from oven and reduce oven temperature to 325°F (160°C).

In a large bowl with an electric mixer, beat the softened cream cheese until it is completely smooth and fluffy (about 2 minutes).

Gradually beat in the granulated sugar until well combined, scraping down the sides of the bowl often. Beat in the sour cream, vanilla extract, and apple pie spice.

Add the eggs one at a time, mixing only until just combined after each egg. Do not overmix the batter once the eggs are in.

Pour the filling over the pre-baked crust.

Place the foil-wrapped springform pan into the center of a large roasting pan. Carefully pour boiling water into the roasting pan until it reaches about halfway up the sides of the springform pan.

Bake for 60–75 minutes. The cheesecake is done when the edges are set and slightly puffed, but the center 2–3 inches are still slightly jiggly.

Turn the oven off, prop the oven door open slightly, and let the cheesecake cool inside the oven for 1 hour.

Remove the pan from the water bath, remove the foil, and let it cool to room temperature on a cooling rack (about 1 hour).

Cover and refrigerate for at least 6 hours, or preferably overnight.

Caramel Sauce: In a medium saucepan, combine the sugar and water. Cook over medium heat without stirring until the sugar dissolves and the liquid turns a rich amber color (about 8–10 minutes).

Remove from heat and quickly whisk in the butter until melted. Slowly pour in the warm heavy cream (it will bubble vigorously). Stir until smooth. Whisk in the coarse sea salt. Set aside to cool.

Apple Topping: In a large skillet, melt the butter over medium heat. Add the apple slices and cook for 5 minutes. Stir in the brown sugar, cinnamon, and lemon juice. Cook for another 5–8 minutes, until the apples are tender but still hold their shape. Let the topping cool to room temperature.

Once the cheesecake is fully chilled, run a thin knife around the inside edge of the pan and gently remove the springform ring.

Spoon the cooled apple topping over the cheesecake.

Drizzle the top with the salted caramel sauce. Slice and serve.