Preheat the oven to 350 degrees. Spray a 9-inch pie pan with cooking spray.
Combine the graham cracker crumbs with 6 tablespoons melted butter. Press firmly into the prepared pie pan, going up the sides of the pan. Bake for 8 to 10 minutes or until brown and fragrant. Leave the oven on.
Place the sweet potatoes in a pot of salted cold water, bring to a boil, and let boil for 5 to 10 minutes or until very tender. Drain the sweet potatoes and put in the bowl of a food processor and puree until smooth. Add the remaining butter, brown sugar, eggs, half-and-half, vanilla, cinnamon, and nutmeg. Process until fully combined, scraping the sides of the bowl once or twice.
Pour the mixture into the pie crust and bake for 45 minutes or until the filling looks set. Let the pie cool, then refrigerate until cold, about 2 hours.
Preheat the broiler to high and position an oven rack in the top third of the oven.
Top with marshmallows and broil for about 1 minute or until the marshmallows swell and brown.