Step 1: Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides for easy removal.
Step 2: Prepare the crust. In a medium bowl, combine graham cracker crumbs, ¼ cup granulated sugar, and melted butter. Mix until well combined. Press the mixture firmly into the bottom of the prepared baking pan. Bake for 8-10 minutes, then remove and let cool slightly.
Step 3: While the crust is baking, prepare the apple filling. In a separate bowl, combine diced apples, 2 tablespoons granulated sugar, 1 teaspoon cinnamon, nutmeg, and lemon juice. Toss to coat evenly.
Step 4: Prepare the cheesecake filling. In a large bowl, using an electric mixer, beat softened cream cheese and ½ cup granulated sugar until smooth and creamy. Beat in eggs one at a time, then stir in vanilla extract until just combined. Do not overmix.
Step 5: Spread the cream cheese mixture evenly over the pre-baked graham cracker crust. Then, evenly distribute the spiced apple mixture over the cheesecake layer.
Step 6: Prepare the streusel topping. In a small bowl, combine flour, brown sugar, and ¼ teaspoon cinnamon. Cut in the cold butter with a pastry blender or your fingertips until the mixture resembles coarse crumbs. Sprinkle the streusel evenly over the apple layer.
Step 7: Bake for 40-50 minutes, or until the cheesecake is set around the edges and slightly jiggly in the center, and the streusel is golden brown.
Step 8: Remove from oven and let cool completely on a wire rack. Once fully cooled, transfer to the refrigerator and chill for at least 4 hours, or preferably overnight, before cutting.
Step 9: Before serving, warm the caramel sauce slightly if it's too thick, then drizzle generously over the chilled bars. Cut into squares and serve.