Preheat oven to 350°F (175°C). Wrap the outside of a 9-inch springform pan with two layers of heavy-duty aluminum foil, ensuring no water can get in.

In a medium bowl, combine the graham cracker crumbs, 1/4 cup brown sugar, and 1/2 tsp cinnamon. Pour in the melted butter and stir until the mixture is fully moistened and resembles wet sand.

Press the crumb mixture firmly and evenly into the bottom and about 1 inch up the sides of the prepared pan. Use the bottom of a glass to pack it tightly.

Bake the crust for 10 minutes. Remove and let it cool completely on a wire rack while you prepare the filling.

In the large bowl of a stand mixer fitted with the paddle attachment, beat the room temperature cream cheese on medium-low speed until completely smooth with no lumps, about 2-3 minutes. Scrape down the sides and bottom of the bowl frequently.

Add the granulated sugar and 1/4 cup brown sugar. Beat on low speed until combined and smooth. Add the flour and salt and mix until just combined.

On low speed, add the eggs one at a time, mixing just until the yellow of the yolk disappears. Do not overmix. Scrape the bowl after each addition.

Gently stir in the sour cream and vanilla extract on low speed until just combined. The batter should be smooth and silky.

Pour the filling over the cooled crust and spread into an even layer.

Place the foil-wrapped springform pan into a large roasting pan. Carefully pour hot water into the roasting pan to come about halfway up the sides of the springform pan. This water bath prevents cracks.

Bake for 65-70 minutes. The edges will be set, but the center will have a slight jiggle. It should not be liquidy.

Turn off the oven, crack the door open with a wooden spoon, and let the cheesecake cool slowly in the oven for 1 hour. This gentle cooling process is key to a perfect texture.

Remove the cheesecake from the water bath, remove the foil, and let it cool completely at room temperature. Once cool, cover loosely with plastic wrap and refrigerate for at least 6 hours, but preferably overnight.

For the Sautéed Apples: In a large skillet, melt 2 tbsp of butter over medium heat. Add the diced apples, 1/2 cup brown sugar, 1 tsp cinnamon, and lemon juice. Cook, stirring occasionally, until apples are tender, about 8-10 minutes.

Stir in the cornstarch slurry and cook for 1 more minute until the sauce thickens. Remove from heat and let the apple topping cool completely to room temperature.

For the Caramel Drizzle: In a small saucepan over medium heat, melt 1/2 cup of butter. Stir in 1 cup of brown sugar until combined. Bring to a gentle boil, then stir in the heavy cream. Let it boil for 1 minute, stirring constantly. Remove from heat and stir in the vanilla extract and sea salt. Let the caramel cool and thicken for at least 20 minutes before using.

Once the cheesecake is fully chilled, carefully run a thin, sharp knife around the edge before releasing the springform pan's sides.

Spread the cooled sautéed apples evenly over the top of the cheesecake.

Drizzle generously with the homemade caramel sauce just before serving. Slice with a large, hot knife, wiping it clean between each cut.