In a large pot, toss sliced peaches with lemon juice, brown sugar, sugar, corn starch, cinnamon, and nutmeg. Cook over medium-high heat for about 8-10 minutes until soft. Set aside to cool.

Line the bottom of a springform pan with parchment paper and lightly spray with non-stick spray. Preheat your oven to 425°F.

In a bowl, mix graham cracker crumbs with melted butter until combined. Press mixture into the bottom of the pan and chill.

Beat softened cream cheese, sugar, and vanilla until smooth. Mix in sour cream and corn starch, then add beaten eggs one at a time on low speed. Pour half of the mixture over the chilled crust.

Place the springform pan into a roasting pan; add hot water until it reaches halfway up the side of the springform pan. Bake at 425°F for 13-15 minutes until the top is set, then reduce the oven temperature to 350°F.

Arrange peach slices on top of the cheesecake layer. Spoon remaining cheesecake mixture over the peaches and smooth it out. Bake for another 40-45 minutes until slightly jiggly in the center.

Combine flour, brown sugar, white sugar, and baking powder in a bowl. Cut in cold butter until the mixture resembles coarse crumbs. Add boiling water and mix until combined.

Once the cheesecake is close to being done, add more peach slices and spoon the cobbler topping evenly. Bake for another 20-25 minutes until golden brown.

Turn off the oven and let the cheesecake sit inside with the door cracked for about an hour. Cool, then refrigerate for at least 4-6 hours or overnight.

Run a knife around the edges, release the sides of the springform pan, and slide it onto a serving plate. Top with any remaining peaches.