Preheat the oven to 325°F.

In a medium bowl, combine graham cracker crumbs, melted butter, and 1/4 cup granulated sugar. Mix until well combined.

Press the mixture firmly into the bottom of a 9-inch springform pan to form the crust. Bake for 10 minutes, then remove from the oven and let cool.

In a large mixing bowl, beat the softened cream cheese with 1 cup granulated sugar and vanilla extract until smooth and creamy.

Add the eggs one at a time, mixing well after each addition. Pour the cream cheese mixture over the cooled crust.

In another bowl, toss the diced apples with cinnamon and nutmeg. Spread the apple mixture evenly over the cream cheese layer.

In a separate bowl, combine brown sugar, rolled oats, and flour. Add melted butter and mix until crumbly. Sprinkle the oat mixture over the apples.

Bake the cheesecake for 55-60 minutes, or until the edges are set and the center has a slight jiggle.

Turn off the oven and let the cheesecake cool in the oven with the door slightly ajar for 1 hour.

Remove from the oven and refrigerate for at least 4 hours, preferably overnight, before serving.