1. Combine Wet Ingredients: In a large mixing bowl, whisk together your active sourdough starter, warm water, granulated sugar, melted butter, and egg until well combined. The mixture should look slightly milky and uniform.

2. Add Dry Ingredients: Gradually add the salt and 3 1/2 cups of all-purpose flour to the wet ingredients. Mix with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. It will be sticky at this stage.

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 5-7 minutes. The dough should become smooth, elastic, and less sticky. If it’s too sticky to handle, add a tiny bit more flour, one tablespoon at a time, but avoid adding too much.

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 spot for 4-6 hours, or until doubled in size. Alternatively, for a slower rise and deeper flavor, you can refrigerate the dough overnight (8-12 hours).

5. Shape the Rolls: Once the dough has risen, gently punch it down to release the air. Turn the dough out onto a lightly floured surface. Divide the dough into 12 equal pieces. For each piece, gently form it into a smooth, round ball by pulling the edges underneath and pinching them together at the bottom.

6. Second Rise (Proofing): Arrange the shaped rolls in a lightly greased 9×13-inch baking dish, leaving a little space between each roll. Cover the dish loosely with plastic wrap or a clean towel and let the rolls rise in a warm spot for another 1-2 hours, or until they look puffy and have nearly doubled in size.

7. Bake the Rolls: Preheat your oven to 375 F (190 C) during the last 15 minutes of the second rise. Bake the rolls for 20-25 minutes, or until they are golden brown on top and sound hollow when tapped on the bottom.

8. Finish and Serve: As soon as the rolls come out of the oven, brush them generously with the remaining 2 tablespoons of melted butter. This adds shine and a lovely buttery flavor. Let them cool slightly before serving warm.