Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving overhang on the long sides for easy lifting.
Make the crust: whisk the flour and brown sugar in a large bowl. Cut in the cold cubed butter with a pastry cutter or your fingertips until coarse crumbs form. Press firmly and evenly into the prepared pan. Bake 15 minutes until lightly golden at the edges.
While the crust bakes, make the cheesecake filling: beat the softened cream cheese and granulated sugar on medium speed until completely smooth, about 2 minutes. Add the sour cream and vanilla and beat to combine. Add the eggs one at a time on low speed, then the flour — mix just until smooth, do not overbeat.
Toss the diced apples with the sugar, cinnamon, and lemon juice in a medium bowl until evenly coated.
Make the streusel: combine the oats, flour, brown sugar, and cinnamon. Cut in the cold butter until pea-sized clumps form.
Pour the cheesecake filling over the hot crust and smooth the top. Scatter the cinnamon apples evenly over the filling, then sprinkle the streusel over everything.
Bake 35-40 minutes, until the edges are set and the center has only a slight jiggle. Cool completely in the pan on a wire rack, about 1 hour.
Refrigerate at least 4 hours (or overnight). Lift out with the parchment sling, drizzle generously with caramel sauce, and cut into 24 bars with a sharp knife, wiping the blade clean between cuts.