Preheat your oven to 350°F (175°C). Grease and line an 8×8-inch square baking pan with parchment paper, leaving a bit of overhang on two opposite sides to make lifting the bars out easier later.
In a small bowl, mix together the flour, brown sugar, granulated sugar, and cinnamon until everything is evenly combined and no lumps remain. Stir in the melted butter until the mixture becomes crumbly and resembles damp sand. Set aside.
Crust
In a food processor, pulse the flour, powdered sugar, and salt a few times to combine. Add in the cold, diced butter and pulse again until the texture looks like coarse crumbs, with some small butter pieces throughout. Pour the mixture into the prepared pan and press it down evenly to form the crust.
Bake for 18–20 minutes, or until the edges are lightly golden and the crust has set. Remove from the oven and let it cool slightly while you prepare the filling.
Cheesecake Filling
In a medium bowl, beat the softened cream cheese until smooth. Add the heavy cream, granulated sugar, flour, and vanilla extract (or vanilla bean paste), and mix until well blended. Add the egg and stir just until fully incorporated.
Apple Layer
In a small bowl, combine the diced apples with cinnamon, 1 tablespoon of granulated sugar, and a squeeze of lemon juice. Toss until the apples are coated.
Spread the cheesecake mixture over the baked crust. Layer the cinnamon-sugar apples evenly on top, then sprinkle the reserved streusel topping over the apples.
Bake for 35–40 minutes, or until the center is set and the top is lightly golden. Let the bars cool completely in the pan on a wire rack.
Transfer to the refrigerator and chill for at least 2 hours to allow everything to firm up. When ready to serve, lift the bars out using the parchment overhang and slice into squares. Enjoy!