1. 1. Combine Wet Ingredients: In a large mixing bowl, whisk together the active sourdough starter, warm milk, mashed cooked potato, granulated sugar, egg, melted butter, and salt until well combined. The mixture might look a little lumpy from the potato, which is perfectly normal.

2. 2. Add Flour and Yeast: Gradually add the all-purpose flour, one cup at a time, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. If using instant yeast, sprinkle it in with the first cup of flour. Once all the flour is added, continue mixing until the dough comes together.

3. 3. Knead the Dough: Turn the dough out onto a lightly floured surface and knead for 8-10 minutes, or use a stand mixer with a dough hook on medium speed for 6-8 minutes, until the dough is smooth, elastic, and no longer sticky. It should spring back when lightly poked.

4. 4. First Rise (Bulk Fermentation): Lightly grease a clean bowl with a little oil. Place the dough in the bowl, turning it once to coat. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place until doubled in size. This can take anywhere from 4 to 8 hours at room temperature, or you can refrigerate it overnight (8-12 hours) for a slower, more flavorful rise.

5. 5. Shape the Rolls: Once the dough has doubled, gently punch it down to release the air. Turn the dough out onto a lightly floured surface and divide it into 12-16 equal pieces, depending on your desired roll size. Shape each piece into a smooth ball by gently pulling the edges underneath and rolling it against the counter with the palm of your hand.

6. 6. Second Rise (Proofing): Arrange the shaped rolls in a greased 9×13-inch baking dish, leaving a little space between them. Cover the dish loosely with plastic wrap or a clean kitchen towel and let the rolls rise in a warm place for another 1-2 hours, or until they are visibly puffy and nearly doubled in size. They should look soft and pillowy.

7. 7. Bake the Rolls: Preheat your oven to 375 F (190 C). Once preheated, remove the cover from the rolls and bake for 20-25 minutes, or until they are golden brown on top and cooked through. The internal temperature should reach 200-210 F (93-99 C).

8. 8. Finish and Serve: As soon as the rolls come out of the oven, brush the tops with the additional 2 tablespoons of melted butter. This adds shine and a lovely buttery flavor. Let them cool in the pan for a few minutes before serving warm.