Preheat oven to 325°F (160°C). Grease a 9-inch springform pan. Wrap the outside bottom of the springform pan tightly with heavy-duty aluminum foil to prevent water from seeping in during the water bath.

In a medium bowl, combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter. Mix until evenly moistened.

Press the mixture firmly into the bottom of the prepared springform pan. Bake for 10 minutes. Remove from oven and let cool slightly while preparing the filling.

In a large mixing bowl, using an electric mixer on medium speed, beat the softened cream cheese until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl.

Gradually add 1 cup granulated sugar and beat until just combined, scraping the bowl as needed. Do not overmix.

Stir in the sour cream and vanilla extract until smooth.

Add the eggs one at a time, beating on low speed until just incorporated after each addition. Be careful not to overbeat, as this can introduce too much air and cause cracks in the cheesecake.

Pour the cheesecake filling over the cooled crust in the springform pan. Gently tap the pan on the counter a few times to release any large air bubbles.

Place the foil-wrapped springform pan into a larger roasting pan. Carefully pour hot water into the roasting pan until it comes halfway up the sides of the springform pan.

Bake for 60-70 minutes, or until the edges are set but the center still jiggles slightly when gently shaken. Turn off the oven, prop the door open slightly, and let the cheesecake cool in the water bath for 1 hour.

Carefully remove the springform pan from the water bath and remove the foil. Let it cool completely on a wire rack at room temperature. Once cool, cover loosely with plastic wrap and refrigerate for at least 6 hours, or preferably overnight.

In a large skillet, melt 2 tbsp butter over medium heat. Add the sliced apples and cook for 5-7 minutes, stirring occasionally, until they start to soften.

Stir in the brown sugar, cinnamon, nutmeg, and lemon juice. Cook for another 3-5 minutes until the apples are tender but still hold their shape.

In a small bowl, whisk together cornstarch and water to create a slurry. Pour the slurry into the skillet with the apples and stir constantly until the sauce thickens, about 1-2 minutes.

Remove from heat and let the apple topping cool completely.

In a medium heavy-bottomed saucepan, combine 1 cup granulated sugar and 1/4 cup water. Stir gently to moisten all the sugar.

Cook over medium-high heat without stirring. Watch carefully as the sugar will begin to bubble and then change color. Swirl the pan occasionally to ensure even cooking. Continue cooking until the caramel turns a deep amber color (about 8-10 minutes).

Once the desired color is reached, immediately remove from heat. Carefully and slowly pour the warm heavy cream into the hot caramel while whisking constantly. Be extremely cautious as the mixture will bubble up vigorously.

Add the room temperature butter pieces, one at a time, whisking until fully incorporated and the sauce is smooth. Stir in the flaky sea salt.

Let the salted caramel cool completely before using. It will thicken as it cools.

Once the cheesecake is fully chilled, run a thin knife around the edge of the pan before releasing the springform ring.

Spoon the cooled spiced apple pie topping over the top of the cheesecake, spreading it evenly.

Drizzle generously with the cooled salted caramel sauce. You can save some caramel for individual servings if desired.

Slice and serve immediately. Store leftover cheesecake in the refrigerator.