Make the Brown Sugar Shortbread:
Preheat oven to 325°F (160°C). Spray a 9×13-inch pan with nonstick spray, line with parchment paper, then spray again with nonstick spray. In the bowl of an electric mixer, cream the butter and brown sugar until light and fluffy. Mix in vanilla bean paste or extract. Gradually add flour and salt, mixing just until combined. Press dough evenly into the prepared pan and bake for 20 minutes, rotating the pan halfway through. Remove from the oven and set aside to cool. Increase oven temperature to 350°F (175°C).
Prepare the Crisp Topping:
In a food processor, pulse flour, brown sugar, salt, and cinnamon just to mix. Add cold, cubed butter and pulse until butter pieces are the size of small peas. Transfer mixture to a bowl, stir in oats, and place in the freezer until ready to use.
Prepare the Cheesecake Layer:
In the bowl of an electric mixer, beat cream cheese and both sugars on medium speed until smooth. Add eggs, one at a time, followed by vanilla bean paste and whiskey (if using), mixing well. Set aside.
Prepare the Apple Layer:
In a bowl, toss diced apples with granulated sugar, cinnamon, and nutmeg until evenly coated.
Assemble the Bars:
Pour cheesecake mixture over the baked shortbread crust. Layer apples evenly on top, then sprinkle with the crisp topping. Bake at 350°F for about 35 minutes, rotating the pan halfway through, until the top is golden and the cheesecake layer is set.
Cool and Serve:
Allow bars to cool to room temperature, then refrigerate. To slice, lift bars from the pan using parchment overhang and cut into squares with a sharp knife. Store in an airtight container in the refrigerator.