Prepare Sweet Potato: Bake or boil the sweet potato until soft. Mash until smooth and set aside 1 cup for the recipe.
Proof the Yeast: In a large bowl, combine the lukewarm milk and yeast. Let it sit for 5-10 minutes until foamy.
Combine Wet Ingredients: Add the sugar, salt, melted butter, egg, and mashed sweet potato to the yeast mixture. Mix well until combined.
Add Flour: Gradually add the flour, 1/2 cup at a time, mixing until a soft dough forms. Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until smooth and elastic. If the dough is too sticky, add more flour, 1 tablespoon at a time.
First Rise: Place the dough in a lightly oiled bowl, turning to coat. Cover with plastic wrap and let rise in a warm place for 1-1.5 hours, or until doubled in size.
Shape the Rolls: Punch down the dough and turn it out onto a lightly floured surface. Divide the dough into 12 equal pieces. Roll each piece into a smooth ball and place them in a greased 9x13 inch baking dish.
Second Rise: Cover the rolls with a clean kitchen towel and let rise in a warm place for 30-45 minutes, or until puffy.
Bake: Preheat oven to 375°F (190°C). If desired, brush the tops of the rolls with the egg wash. Bake for 20-25 minutes, or until golden brown.
Cool and Serve: Let the rolls cool in the baking dish for a few minutes before transferring them to a wire rack to cool completely. Serve warm and enjoy!