01 - Preheat the oven to 350°F (175°C). Line the base of a 9-inch springform pan with parchment paper.
02 - In a bowl, combine graham cracker crumbs, melted butter, granulated sugar, and ground cinnamon. Press the mixture firmly and evenly into the base of the prepared pan. Bake for 10 minutes, then allow to cool slightly.
03 - In a skillet over medium heat, combine diced apples, brown sugar, lemon juice, cinnamon, ginger, cardamom, cloves, allspice, black pepper, and salt. Sauté for 5 to 7 minutes until the apples are tender but not mushy. Set aside to cool to room temperature.
04 - In a large mixing bowl, beat softened cream cheese with granulated sugar using an electric mixer until smooth and fluffy. Add eggs one at a time, mixing well after each addition. Blend in sour cream, vanilla extract, and all-purpose flour until the mixture is cohesive and velvety.
05 - Pour half of the cheesecake batter over the cooled crust. Distribute half of the chai-spiced apples over the batter. Gently add the remaining cheesecake batter and arrange the rest of the apples on top, swirling them lightly into the batter with a spatula.
06 - In a separate bowl, combine rolled oats, flour, brown sugar, ground cinnamon, and salt. Cut the cold, cubed butter into the mixture with a pastry cutter or fork until a crumbly texture forms. Sprinkle the oat mixture evenly over the top layer.
07 - Bake in the center of the oven for 60 to 70 minutes, or until the edges are set and the center is just slightly wobbly.
08 - Remove from oven and allow to cool fully at room temperature. Cover and refrigerate for at least 4 hours, or overnight, before slicing and serving.