First, preheat your oven to 350 degrees Fahrenheit. Then, sauté half of the peaches in a skillet over low medium heat. Slice 4 of the peaches. Add the peaches, sugar, cinnamon, and nutmeg to the warm skillet. You may need to add a splash of water to prevent burning. Cook for 3 to 4 minutes, until the peaches are coated in cinnamon sugar and starting to look soft. Remove from heat and set aside.
Preheat your oven to 350 degrees Fahrenheit.
Next, make the graham cracker crust. Add the graham crackers to a food processor. Process until fine and crumbly. Stir in the melted butter. The mixture should resemble wet sand.
Press this mixture down into a lined 8 inch springform cheesecake pan. Note: I like to save about 2 tablespoons of this mixture for topping the cheesecake after it bakes.
Bake this crust at 350 degrees Fahrenheit for 10 minutes. Then, remove from the oven.
At this point, I like to start boiling 4 cups of water for the water bath. Use an oven safe pot.
While the crust bakes, make the cheesecake filling. Add the room temperature cream cheese to a large mixing bowl. Use an electric mixer to whip until smooth and creamy. Add in the 4 eggs and mix until just barely combined. Do not over mix.
Then, add in the sugar, Greek yogurt, vanilla, and arrowroot powder. Stir until just barely combined.
Pour half of this cheesecake mixture on top of the crust. Top with the sautéed peaches. Then, pour the remaining cheesecake batter on top. Smooth into an even layer.
Place the pot of boiling on the lowest rack of your oven. Then, place the cheesecake pan on the rack directly above the water bath.
Bake for 1 hour 30 minutes or until the cheesecake is slightly jiggly.
Finally, turn the oven off. Open the oven door slightly and leave the cheesecake inside for 1 hour. This allows the cheesecake to slowly cool down and helps prevent cracks.
Cool for at least 4 hours, ideally overnight.
When ready to serve, sauté the remaining peaches on the stovetop. Serve the cheesecake with those peaches on top and a sprinkle of graham cracker crumbs if desired!