Preheat your oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later.
Combine the graham cracker crumbs, sugar, and salt in a medium bowl. Pour in the melted butter and stir until the mixture resembles wet sand. Press firmly into the bottom of the prepared pan, creating an even layer.
Bake the crust for 8-10 minutes until lightly golden. Allow it to cool slightly while preparing the next layers.
In a large bowl, beat the cream cheese until smooth and creamy. Add the sugar and beat until well combined, about 2 minutes. Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract and sour cream until just combined.
Toss the sliced apples with lemon juice to prevent browning. In a separate bowl, mix the brown sugar, cinnamon, nutmeg, and cornstarch. Sprinkle over the apples and toss until evenly coated.
Pour the cheesecake mixture over the cooled crust, spreading evenly. Arrange the spiced apple slices in an overlapping pattern on top of the cheesecake layer.
In a medium bowl, combine the flour, oats, brown sugar, salt, and cinnamon. Cut in the cold butter using a pastry cutter or your fingers until the mixture resembles coarse crumbs with pea-sized pieces of butter visible.
Sprinkle the crisp topping evenly over the apple layer. Bake for 45-50 minutes, or until the cheesecake is set around the edges but still slightly jiggly in the center. The crisp topping should be golden brown.
Allow the bars to cool completely at room temperature, about 1 hour. Then refrigerate for at least 4 hours or overnight.
Use the parchment paper overhang to lift the bars out of the pan. With a sharp knife dipped in hot water and wiped clean between cuts, slice into 16 bars.