01 -  Preheat the oven to 350°F. Line an 8x8-inch baking pan with parchment paper, ensuring some overhang for easy removal. 
 02 -  In a medium bowl, combine all-purpose flour, granulated sugar, salt, and melted butter until a crumbly dough develops. Press the mixture evenly into the prepared pan. Bake for 10 minutes. 
 03 -  Using a bowl and electric mixer or whisk, beat cream cheese and granulated sugar until smooth. Add in the egg and vanilla extract; blend until just combined. Pour and spread evenly over the baked crust. 
 04 -  In a separate bowl, toss diced apples with brown sugar, ground cinnamon, nutmeg, and lemon juice to evenly coat. Distribute the apple mixture over the cheesecake layer. 
 05 -  In another bowl, combine all-purpose flour, rolled oats, brown sugar, and cinnamon. Add cold, cubed butter and work into the dry mixture using fingers or a pastry blender until coarse crumbs form. Sprinkle the topping evenly over the apple layer. 
 06 -  Bake for 35 to 40 minutes until the topping turns golden brown and the center is set. Cool completely in the pan, then refrigerate for at least 2 hours before cutting into bars.