1. Combine the Wet Ingredients: In a large mixing bowl, whisk together your active sourdough starter, warm milk, granulated sugar, salt, and the large egg until well combined. The mixture should look slightly frothy from the starter.

2. Add Flour and Butter: Gradually add the 4 cups of all-purpose flour to the wet ingredients, mixing with a wooden spoon or Danish dough whisk until a shaggy dough forms. Pour in the 1/4 cup of melted unsalted butter and continue to mix until the butter is mostly incorporated and the dough comes together.

3. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for 5-7 minutes until the dough is smooth, elastic, and no longer sticky. It should pass the “windowpane test” where you can stretch a small piece thin enough to see light through it without tearing.

4. First Rise (Overnight Cold Proof): Lightly grease the mixing bowl with a little oil. Place the kneaded dough into the bowl, turning it once to coat. Cover the bowl tightly with plastic wrap or a damp kitchen towel. Transfer the bowl to the refrigerator and let it rise overnight for 8-12 hours. The dough should visibly increase in size, though not necessarily double, due to the cold temperature.

5. Shape the Rolls and Second Rise: The next morning, remove the dough from the refrigerator. Gently punch down the dough to release the air. Turn it out onto a lightly floured surface and divide it into 12 equal pieces. Shape each piece into a smooth, round roll. Arrange the rolls in a lightly greased 9×13 inch baking dish, leaving a little space between them. Cover the dish with plastic wrap or a damp towel and let the rolls rise at room temperature for 1-2 hours, or until they look puffy and have nearly doubled in size.

6. Bake the Rolls: Preheat your oven to 375 F (190 C) about 20 minutes before the second rise is complete. Once the rolls are ready, remove the cover and bake for 18-22 minutes, or until they are golden brown on top and sound hollow when tapped.

7. Prepare and Apply the Butter Glaze: While the rolls are baking, melt the remaining 2 tablespoons of unsalted butter in a small saucepan or microwave-safe bowl. Whisk in the 1/4 cup of powdered sugar until smooth. As soon as the rolls come out of the oven, brush the warm butter glaze generously over the tops of the hot rolls.

8. Serve and Enjoy: Let the rolls cool slightly in the pan for a few minutes before serving warm.