Preheat the oven to 350°F. Line a 9x13-inch baking dish with foil, spray with cooking spray, and set aside.
In a large bowl, stir together the 2 cups flour, powdered sugar, and ½ tsp cinnamon until combined.
Slice in the 1 cup softened butter and cut it into the dry ingredients with a pastry cutter until combined.
Press the dough evenly into the bottom of the baking dish. Bake for 20 minutes until set, then set aside.
Layer the sliced peaches over the crust.
In a large bowl, beat the cream cheese with an electric hand mixer until smooth. Add the ¾ cup granulated sugar and mix until combined.
Add the eggs one at a time, mixing each in before adding the next. Mix in the vanilla.
Pour the cream cheese mixture over the peaches.
In another bowl, stir together the 1½ cups flour, brown sugar, ¼ cup granulated sugar, 1 tsp cinnamon, nutmeg, and salt until combined.
Add the melted butter and stir with a fork until the mixture forms crumbles.
Sprinkle the crumble topping evenly over the cheesecake layer.
Bake for 45–55 minutes until the top is lightly golden brown and the cheesecake is set (a very slight jiggle in the center is okay). Cool completely on the counter, then refrigerate until set.