Preheat your oven to 350 degrees Fahrenheit. Line an 8×8 inch square baking pan with parchment paper, leaving a little overhang on the sides. This makes it much easier to lift the bars out once they have cooled and set.
In a medium bowl, combine the graham cracker crumbs and the melted butter. Stir until the mixture looks like wet sand. Press the mixture firmly into the bottom of your prepared baking pan, using the bottom of a measuring cup to ensure it is even. Bake the crust for 8 minutes, then remove it from the oven and let it cool slightly while you prepare the filling.
In a large mixing bowl, beat the softened cream cheese and granulated sugar together until the mixture is smooth and fluffy. Add the eggs one at a time, beating well after each addition. Stir in the alcohol-free vanilla. Pour this creamy mixture over the par-baked crust and spread it out into an even layer.
In a small bowl, toss the diced apples with the cinnamon and nutmeg until they are well coated. In a separate bowl, whisk together the brown sugar, flour, and oats. Use a pastry cutter or your fingers to work the cold, cubed butter into the flour mixture until it resembles coarse crumbs. Gently layer the spiced apples over the cheesecake filling, then sprinkle the crumble mixture generously over the top.
Place the pan back into the oven and bake for 40 to 45 minutes. You want the edges to be set and the crumble to be golden brown, though the center might still have a very slight jiggle. Do not overbake, as the cheesecake will continue to firm up as it cools.
Allow the bars to cool to room temperature on a wire rack. Once cooled, place the pan in the refrigerator for at least 3 to 4 hours, or ideally overnight. This chilling process is essential for the bars to set properly so you can get those clean, beautiful slices.
