1. Combine Wet Ingredients: In a large mixing bowl, whisk together the active sourdough starter, warm water, granulated sugar, and lightly beaten egg until well combined. The mixture will look a bit cloudy.

2. Add Dry Ingredients: Add the all-purpose flour, instant yeast, and fine sea salt to the wet ingredients. Mix with a wooden spoon or a Danish dough whisk until a shaggy dough forms and no dry streaks of flour remain.

3. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for 8-10 minutes until the dough is smooth, elastic, and passes the windowpane test (you can stretch a small piece thin enough to see light through it without tearing). Alternatively, use a stand mixer with a dough hook for 6-8 minutes on medium speed.

4. First Rise (Overnight Bulk Fermentation): Place the kneaded dough in a lightly oiled bowl, turning it once to coat. Cover the bowl tightly with plastic wrap or a damp kitchen towel. Refrigerate for 8-12 hours, or overnight. This slow, cold fermentation develops flavor and makes the dough easier to handle.

5. Shape the Rolls: The next day, remove the dough from the refrigerator. It should have risen significantly. Gently punch down the dough to release the air. Turn it out onto a lightly floured surface and divide it into 12-16 equal pieces (about 60-70 grams each for 12 rolls). Shape each piece into a tight ball by pulling the edges under and rolling it against the counter with the palm of your hand.

6. Second Rise (Proofing): Arrange the shaped rolls in a lightly 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 them rise in a warm place for 1-2 hours, or until they are visibly puffy and almost doubled in size. They should feel light and airy.

7. Bake the Rolls: Preheat your oven to 375 F (190 C) during the last 20 minutes of the second rise. Just before baking, brush the tops of the rolls with melted butter. Bake for 20-25 minutes, or until the rolls are golden brown on top and cooked through. An internal temperature of 200-210 F (93-99 C) indicates they are done.

8. Cool and Serve: Once baked, remove the rolls from the oven. Brush them again with a little more melted butter for extra shine and flavor. Let them cool in the pan for 5-10 minutes before serving warm.