Preheat the oven to 350°F. Line a 9×13-inch baking pan with parchment paper, leaving some overhang on two sides. Lightly grease any exposed sides of the pan.
Make the crust. In a medium bowl, combine the flour, granulated sugar, and salt. Add the melted butter and mix until a thick, crumbly dough forms.
Press the crust mixture firmly and evenly into the prepared pan. Bake for 12–15 minutes, until set and lightly golden around the edges. Remove from the oven and keep the oven at 350°F.
Peel and core the apples, then dice them into approximately 1/4-inch pieces. Toss with 2 tablespoons granulated sugar, cinnamon, and nutmeg. If the apples release excess liquid, leave the extra liquid behind when assembling the bars.
Make the cheesecake filling. Beat the softened cream cheese and 3/4 cup granulated sugar on medium-low speed until smooth and creamy.
Add the eggs one at a time, mixing on low speed just until incorporated. Mix in the vanilla. Avoid overmixing after adding the eggs.
Make the streusel. Combine the flour, rolled oats, brown sugar, and cinnamon in a medium bowl. Add the melted butter and stir with a fork until coarse crumbs form.
Pour the cheesecake filling over the prebaked crust and spread evenly.
Distribute the cinnamon apple pieces evenly over the cheesecake filling.
Sprinkle the streusel evenly over the apples.
Bake at 350°F for 40–50 minutes. The edges should be set while the center still has a slight jiggle. The center should not look liquid.
Transfer the pan to a wire rack and allow the cheesecake bars to cool completely at room temperature.
Cover and refrigerate for at least 4 hours, preferably overnight, until thoroughly chilled and firm.
Use the parchment overhang to lift the chilled cheesecake from the pan. Cut into 16 bars with a sharp knife, wiping the blade clean between cuts.
Drizzle the bars with caramel sauce just before serving.