Preheat the oven to 400 degrees F (200 degrees C). Line the bottom of a 10-inch springform pan with parchment paper, then close the ring around it for each removal of the cheesecake after baking.
Place walnuts in a bowl and drizzle melted butter on top. Toss until evenly coated. Sprinkle dark brown sugar, cinnamon, and cloves on top and toss nut topping well.
Place sliced apples in a bowl, add lemon juice, and toss well. Add cinnamon and cloves and toss apple topping. Set both toppings aside.
Mix flour, sugar, chopped pecans, and lemon peel together in a bowl until well combined. Cut in butter slowly, 1 tablespoon at a time. Add egg yolk and vanilla extract and mix well. Press crust mixture into the bottom of the prepared springform pan.
Bake in the preheated oven until edges are lightly browned, 10 to 12 minutes. Remove from oven and cool crust on a wire rack. Reduce oven temperature to 325 degrees F (165 degrees C).
Place cream cheese in a bowl and beat with an electric mixer until smooth. Add sugar slowly, 1/4 cup at a time, mixing well to ensure it is dissolved after each addition. Add flour, vanilla extract, lemon juice, and salt.
Combine egg and egg yolks in a bowl and add to cream cheese mixture. Beat in heavy cream and whip on high speed for 2 to 3 minutes. Pour into the cooled crust and decorate with the cinnamon apples. Sprinkle just some of the nut topping on top.
Fill a 9×13-inch baking pan with water and place on the bottom rack of the hot oven.
Bake the cheesecake on the middle rack of the hot oven until set, about 80 minutes.
Turn oven off and let cheesecake sit, untouched, for 1 hour to finish cooking throughout.
Cool on a wire rack until room temperature, about 1 hour. Place cheesecake in the refrigerator for 8 hours to overnight.
Run a knife around the edge of the pan to loosen chilled cheesecake. Remove sides of pan.
Crush remaining nut topping into a crumble and use to decorate around the sides of the cheesecake.
Melt caramel topping in a microwave oven for 30 seconds at a time until pourable. Drizzle on top of cheesecake and top with more walnuts, if desired.
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