Preheat oven to 350 degrees F. Line a cupcake tin with liners. In a small bowl, mix melted butter, sugar and graham cracker crumbs until moist, then press about 1/2-1 tablespoon of crumbs into the bottom of each liner.
In a large bowl, whisk egg and sugar together until combined and no lumps remain. Add in vanilla extract and butter, then whisk in sweet potato. Add in flour, baking soda, salt, cinnamon and nutmeg, then add in milk and stir until combined and smooth. Drop about 1/4 cup of batter on top of each graham cracker crust. Bake for 15-17 minutes, or until cupcakes are set and spring back at the touch. Let cool completely before frosting.
To make frosting: beat butter in the bowl of electric mixer until creamy. Add in fluff and beat for 2-3 minutes, then add in vanilla extract. With the mixer on low speed, add in powdered sugar 1 cup at a time until fully incorporated. Once all the sugar has been added, beat on medium-high speed for 2-3 minutes. If mixture if too runny, add a bit more sugar. If it’s too thick, add a bit of milk one teaspoon at a time. Frost cupcakes and drizzle with caramel sauce and crushed cinnamon pecans.