Preheat the oven to 325°F (160°C).
In a mixing bowl, combine graham cracker crumbs and melted butter. Press into the bottom of a 9-inch springform pan and bake for 10 minutes.
In a large bowl, beat cream cheese and sugar until smooth. Add eggs one at a time, mixing well after each. Incorporate vanilla, cinnamon, and nutmeg.
Fold in half of the apple butter into the cheesecake batter.
Pour cheesecake filling into the cooled crust, swirling in spoonfuls of remaining apple butter.
Place the springform pan in a larger roasting pan with hot water halfway up the sides. Bake for 55-60 minutes.
Turn off the oven and crack the door ajar, letting the cheesecake sit for 1 hour.
Cool at room temperature for 30 minutes, then refrigerate for at least 4 hours.
Remove from the springform pan, slice, and serve with whipped cream and apple butter.