Preheat your oven to 350°F (175°C) and line an 8×8 inch square baking pan with parchment paper, leaving an overhang on the sides.

In a medium bowl, mix the graham cracker crumbs, melted butter, and sugar until it looks like wet sand. Press the mixture firmly into the bottom of the prepared pan.

Bake the crust for 10 minutes, then remove it from the oven and let it cool slightly.

In a large bowl, beat the softened cream cheese and sugar together until smooth and creamy. Add the eggs one at a time, followed by the sour cream and vanilla extract. Mix until just combined.

Pour the cheesecake mixture over the pre-baked crust and spread it out evenly with a spatula.

In another bowl, toss the diced apples with sugar, cinnamon, and nutmeg until well coated. Layer the apples over the cheesecake filling.

Prepare the crumble by mixing the flour, oats, and brown sugar. Work the cold butter into the mixture until it forms pea-sized crumbs.

Sprinkle the crumble evenly over the apple layer.

Bake for 40 to 45 minutes, or until the edges are set and the top is golden. The center should still have a slight jiggle.

Allow the bars to cool to room temperature, then refrigerate for at least 4 hours (or overnight) before slicing into squares.