Preheat oven to 325°F. Wrap the outside of a 9-inch springform pan with 2 layers of heavy-duty foil. Lightly grease the inside.
Make the crust: In a bowl, mix graham cracker crumbs, 0.25 cup sugar, and 0.5 tsp cinnamon. Stir in melted butter until the mixture resembles wet sand. Press firmly into the bottom of the pan. Bake 10 minutes; set aside to cool slightly.
Beat the cream cheese on medium speed until completely smooth, 2 to 3 minutes. Add granulated sugar and brown sugar; beat until fluffy, scraping the bowl.
Mix in sour cream, 1.0 cup apple butter, vanilla, cinnamon, nutmeg, salt, and flour until just combined.
Add eggs one at a time on low speed, blending just until incorporated after each to avoid overmixing.
Pour batter over the crust. Spoon 0.5 cup apple butter in small dollops over the top and swirl with a knife for a marbled look.
Set the pan in a larger roasting pan and pour hot water into the outer pan to reach halfway up the sides of the springform (water bath).
Bake 60 to 65 minutes, until edges are set and the center wobbles slightly. Turn off oven, crack the door, and let cheesecake rest inside 1 hour.
Remove from water bath, discard foil, and cool on a rack until room temperature. Chill at least 4 hours or overnight before slicing.
Unmold, top with caramel sauce and whipped cream if desired, slice, and serve.
Notes
For the cleanest slices, warm a thin knife under hot water and wipe between cuts. Cheesecake keeps well refrigerated for up to 5 days or frozen (well wrapped) for up to 2 months.