If using a whole sweet potato: Peel and chop into 1-inch cubes. Add to a small saucepan, cover with water. Cook over medium-high heat for 20-30 minutes or until fork tender. Drain and mash with a few tablespoons of milk. Measure out 1 cup mashed sweet potatoes. Set aside. 

Heat milk to 115-120°F. Dissolve yeast and 1/2 tsp granulated sugar in warm milk. Allow to proof for 5 minutes. 

Meanwhile, combine 4 cups of flour, salt and remaining sugar in the bowl of a stand mixer. With dough hook attachment in place, turn mixer on low. Add one egg at a time, followed by 6 tablespoons of butter, mashed sweet potatoes and yeast mixture. Increase speed, mixing until dough pulls away from the sides of the bowl. If necessary, add an extra 1/4 cup of flour. 

Transfer dough to a lightly greased large bowl. Cover and allow to rise in a warm location for 90 minutes or doubled in size. 

Grease a 9x13-inch pan. Set aside. 

Divide dough into 12 equal portions. Shape into a ball, pinching the seam together. Place seam side down into prepared pan. Repeat with remaining portions of dough. Lightly spray a sheet of plastic wrap with olive oil or cooking spray. This will prevent the rolls from sticking to the plastic. Cover the rolls and allow to rise in a warm location for an additional 60 minutes. 

Preheat oven to 350°F. Bake rolls for 20-25 minutes or until internal temperature reaches 200°F. 

Immediately brush rolls with melted butter. Serve warm or at room temperature. Store remaining rolls in an airtight container for up to several days.