Preheat the oven to 425 degrees F. Wash the sweet potatoes and dry them off with a paper towel. Prick holes in the sweet potatoes and place onto a baking sheet. Bake for 30-45 minutes, until form tender. Peel the skins and place into a medium bowl.
Add cinnamon, nutmeg, and a pinch of kosher salt. Mash the sweet potatoes until smooth. Allow the sweet potatoes to cool for 15 minutes, until cool to the touch.
Mix together melted butter, brown sugar, cinnamon, and nutmeg in a small bowl.
Remove the ice cream from the packaging and place into the bowl. Use an electric hand mixer to mix the sweet potato mixture and the ice cream together.
Dollop the cinnamon mixture on top and use a toothpick to swirl throughout. Sprinkle the graham cracker pieces on top and swirl again. Cover with plastic wrap and freeze for 1-2 hours.