1. In a large mixing bowl, whisk together the warm milk, active sourdough starter, melted butter, and beaten egg until well combined. The mixture should look slightly milky and uniform.

2. Add the salt and instant yeast to the wet mixture. Gradually add 3 cups of the all-purpose flour, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms.

3. Turn the dough out onto a lightly floured surface. Knead for 5-7 minutes, adding more flour a tablespoon at a time if the dough is too sticky, until it becomes smooth, elastic, and no longer sticks to your hands. It should spring back when lightly poked.

4. Lightly grease a clean bowl with butter. 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 for 1 to 1.5 hours, or until doubled in size.

5. Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface and divide it into 12 equal pieces. Roll each piece into a smooth ball. Arrange the dough balls in a greased 9×13-inch baking dish, leaving a small space between each.

6. Cover the baking dish loosely with plastic wrap or a kitchen towel and let the rolls rise again in a warm place for 30-45 minutes, or until they look puffy and have nearly doubled in size.

7. Preheat your oven to 375 F (190 C) during the last 15 minutes of the second rise. You can brush the tops of the rolls with a little melted butter or an egg wash (one beaten egg with a tablespoon of water) for a golden crust, if desired.

8. Bake for 18-22 minutes, or until the rolls are golden brown on top and sound hollow when tapped on the bottom. Remove from the oven and brush with a little more melted butter for extra shine and flavor, if you like. Let them cool slightly in the pan before serving.