To prepare a candyd sweet potato cupcakes with brown sugar icing recipe, first you will need to prepare the sweet potatoes. Peel and cut the Sweet Potatoes in half lengthwise and scoop out the seeds. Cut the flesh from the skin and add it to the cupcake batter. Fill each cupcake liner with the batter and bake for 18 to 20 minutes or until the toothpick comes out clean. Remove from oven and allow to cool for 5 minutes before frosting.