Roast the sweet potato in the oven and remove the skin and puree into fine paste.
Use room temperature milk and egg. Place the egg in a small bowl of hot ( about 120°F) water for 5 minutes. Warm the milk ( in a saucepan or in the microwave until it is about 90 °F.
In a bowl of kitchen aid stand mixer fitted with the dough-hook attachment combine, sourdough starter, egg, milk, salt, sweet potato puree, yeast, and sugar. Mix everything at low speed until everything is combined well.
To this add bread flour and knead well. Then gradually add softened butter. Dough should pass the windowpane.
Bulk fermentation
Transfer the dough into a large clean bowl, loosely cover the dough with a clean kitchen towel, set aside in warm (80F- 85F ) draft free place about 1 ½ hours. To strengthen the dough, stretch and fold the dough every 30 minutes interval.
Once the bulk fermentation is finished divide and shape the dough.
Shape and bake
Divide the dough into 12 equal pieces of 55g . Line the 9 by 13-inch baking pan with parchment paper or generously butter them .
Divide and shape the dough into small tight round balls. Using lightly floured hands, shape each piece into a ball. Working with one ball at a time, very gently cup your dominant hand over the dough and press it into the work surface while rotating your hand clockwise in a circular motion. The bottom of the roll should stick to the surface a little, anchoring it. Continue the circular motion until you have a tight cohesive ball. Repeat to shape the remaining balls until you finish all the dough.
Cover with a clean kitchen towel and let rise in a warm spot (78° F to 82 °F ) until rolls have grown and when you poke them with fingertip, they should spring back slowly. It takes about 45 minutes to 1 hour.
Bake
Preheat the oven to 350°F. Fill a clean, food-grade spray bottle with water.
Brush the tops of the rolls with half of the melted butter. Place the pan of rolls in the oven, then spray the sides and bottom of the oven generously with water. Immediately close the oven door. Bake for 10 minutes, rotate the pan front to back, and continue baking until the tops of the rolls are deep golden brown, 5 to 7 minutes.
Remove the rolls from the oven and brush with melted butter . This step is optional but it will increase the taste.
Store leftover rolls in a bread box at room temperature for up to 1 day. To store longer, once the rolls are cool, place in an airtight container and freeze for up to 2 weeks. To reheat, warp tightly in aluminum foil and warm in a 250°F oven for 10 to 15 minutes.