Prepare the Baking Pan: Preheat the oven to 350°F (175°C). Line an 8×8-inch or 9×13-inch baking pan with foil and spray with non-stick spray for easy removal.
Make the Crust: In a large mixing bowl, combine the sugar cookie mix and cold butter. Use a pastry blender to mix until the mixture is crumbly. Set aside about 3/4 cup of this mixture. Press the remaining crust mixture into the bottom of the prepared pan. Bake for 10 minutes, then allow it to cool slightly. The crust may look a bit underdone, but it will continue to bake with the other layers.
Prepare the Cheesecake Layer: While the crust cools, mix the softened cream cheese, granulated sugar, flour, vanilla extract, and egg in a separate bowl until smooth and creamy.
Assemble the Layers: Spread the cream cheese mixture evenly over the cooled crust. Spoon the cherry pie filling evenly over the cream cheese layer, making sure to distribute the cherries.
Add the Topping: In a small bowl, mix the reserved crumbly cookie mixture with the toasted sliced almonds. Sprinkle this mixture evenly over the cherry layer.
Final Bake: Place the pan back in the oven and bake for 40 minutes if using an 8×8 pan or 45 minutes if using a 9×13 pan, until the top is lightly golden brown.
Cool and Store: Allow the bars to cool at room temperature for 30 minutes, then chill in the refrigerator for a few hours to set. Store any leftovers in the refrigerator, covered.