In a small bowl, sprinkle yeast over water. Let sit for a minute, then stir to combine. Let sit until frothy, about 10 minutes.
In a small saucepan, heat milk over medium heat. Stir constantly until bubbles begin to rise around the edges. Add sweet potato, sugar, butter, and salt. Continue to stir until butter is melted and mixture is smooth. Remove from heat.
In the bowl of a large food processor fitted with a dough blade or a large bowl, add flour. Mix in warm milk mixture and frothy yeast until a smooth dough forms. It will be sticky and slightly wet. Knead dough on floured surface until soft and elastic. Place in oiled large bowl, cover, and let rise until doubled, 1 1/2-2 hours.
Oil a 9x13 inch pan with at least 1 inch sides. Punch down the risen dough and divide into 16 equal pieces. Roll each piece into a ball and place in oiled pan, 4 to a row. Cover and let rise until doubled, 1 1/2-2 hours.
Preheat oven to 350 degrees Bake rolls in preheated oven until cooked through and golden, 15-20 minutes. Let cool in pan before removing.