Preheat the oven to 350°F (175°C). Grease a 9-inch springform pan.
In a small bowl, mix graham cracker crumbs, 3 tablespoons white sugar, 1/2 teaspoon cinnamon, and melted butter. Press into the bottom of the pan.
In a large bowl, beat the cream cheese with 1/2 cup white sugar and vanilla extract until smooth. Blend in the eggs one at a time. Pour the mixture over the crust.
Toss the apple slices with 1/4 cup sugar and 1/2 teaspoon cinnamon. Arrange on top of the cheesecake layer.
In another bowl, combine flour, brown sugar, oats, and cold butter. Mix until crumbly. Sprinkle over apples.
Bake in the preheated oven until set, about 50 to 60 minutes. Let cool, then refrigerate for at least 4 hours or overnight before serving.