Preheat oven to 350°F (175°C). Wrap a 9-inch springform pan with a double layer of heavy-duty foil. Combine graham cracker crumbs, melted butter, and sugar. Press firmly into the bottom and slightly up the sides of the pan.

Bake for 10 minutes. Let cool completely on a wire rack.

In a large bowl, beat room temperature cream cheese until completely smooth. Gradually add sugar and beat until combined. Add eggs one at a time, mixing on low speed just until combined.

Gently stir in sour cream, vanilla, and flour. Pour filling over the cooled crust.

In one bowl, toss sliced peaches with 1/2 cup brown sugar, cinnamon, and nutmeg. In another bowl, combine 1/2 cup flour, oats, and more brown sugar. Cut in the cold butter until it forms coarse crumbs.

Spoon the peaches over the cheesecake filling, then sprinkle the crumble mixture on top.

Place the springform pan in a large roasting pan and create a water bath by pouring boiling water halfway up the sides of the pan. Bake for 60-70 minutes, until the edges are set but the center has a slight wobble.

Turn off the oven, crack the door, and let the cheesecake cool in the oven for 1 hour. Remove from the water bath and cool completely at room temperature.

Chill in the refrigerator for at least 6 hours or overnight before serving.