In the bowl of an electric mixer, whisk together warm water, yeast and 1/2 tsp granulated sugar. Whisk until yeast dissolves and let rest 5 minutes. Stir in buttermilk, 1/4 cup butter, egg, 1/4 cup sugar, salt and sweet potato puree. Mix in 1 cup flour. Add remaining flour and knead with a dough hook attachment until dough is smooth an elastic (dough should be slightly sticky, but should pull away from the sides of the bowl). Transfer dough to a large buttered mixing bowl and cover with plastic wrap and let rise in a warm place until double, about 1 hour.
Butter a 13" x 9" baking dish, set aside. Punch dough down and divide into 20 pieces (they should be about 1/4 cup each). Roll pieces into balls and place in greased baking dish (I do 5 rows of 4, they will touch vertically). Let rise until double, about 30 minutes. Preheat oven to 400 degrees. Bake rolls 17 - 20 minutes until golden. Remove from oven and brush with melted butter.