Combine graham cracker crumbs, 1/4 cup granulated sugar, and melted butter in a medium mixing bowl.
Press the mixture into the bottom of a 9-inch springform pan to form the crust.
In a large mixing bowl, beat cream cheese and 1 cup granulated sugar until smooth.
Add eggs one at a time, mixing well after each addition.
Mix in vanilla extract and sour cream until combined.
Pour the cream cheese mixture over the crust in the springform pan.
In a small saucepan, combine diced apples, brown sugar, and 1/2 teaspoon cinnamon; cook until apples are tender.
Spoon the apple mixture evenly over the cream cheese layer.
In another bowl, mix rolled oats, flour, remaining cinnamon, and cold cubed butter until crumbly.
Sprinkle the oat mixture over the apple layer.
Bake in the preheated oven for 1 hour or until the cheesecake is set.
Remove from oven and let cool to room temperature.
Refrigerate for at least 4 hours before serving.
Notes
Allowing the cheesecake to fully cool and set in the refrigerator is crucial for achieving the perfect texture, so plan ahead to give it ample resting time. When cutting the cheesecake, use a sharp knife dipped in hot water for clean slices.