In a small saucepan over medium heat, combine the apple, sweetener, water, and cinnamon and bring to a simmer. Cook about 5 minutes, until the apples are tender.

Remove from heat and let cool while preparing the cheesecake bars.

Preheat the oven to 325F.

In a medium bowl, whisk together the almond flour, sweetener, and salt. Stir in the melted butter until the dough begins to clump together.

Press firmly and evenly into the bottom of a 9-inch square metal non-stick baking pan (if your pan is not very good nonstick, you may want to grease it). Bake 10 minutes.

Remove and let cool while preparing the rest of the cheesecake. Reduce the oven temperature to 300F.

In a large bowl, beat the cream cheese until smooth, then beat in the sweetener until well combined.

Beat the eggs in one at a time, scraping down the beaters and the sides of the bowl as necessary. Beat in the extracts until the mixture is smooth.

Pour the cheesecake filling over the cooled crust, then top with the apples, spreading them out for even coverage. Drizzle any liquid from the apples overtop as well.

In another medium bowl, whisk together the almond flour, sweetener, coconut flour, cinnamon, and salt. Stir in the melted butter until the mixture resembles coarse crumbs.

Sprinkle evenly over the cheesecake filling and bake 30 to 40 minutes, until the edges are set but the center still jiggles slightly.

Remove and let cool to room temperature, then refrigerate to firm up, at least 2 hours.