1. Combine the Wet Ingredients: In a large mixing bowl, whisk together your active sourdough starter, warm milk, 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 the all-purpose flour to the wet ingredients. Mix with a sturdy spoon or a dough whisk until a shaggy dough forms. If the dough is still very sticky, add the remaining 1/2 cup of flour, a little at a time, until the dough comes together and is manageable, but still soft.

3. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for about 5-7 minutes. The dough should become smooth, elastic, and less sticky. You’ll know it’s ready when it springs back slowly when gently poked.

4. First Rise (Bulk Fermentation): Lightly grease your mixing 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 for 1.5 to 2 hours, or until it has nearly doubled in size.

5. Shape the Rolls and Second Rise (Proofing): 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. Shape each piece into a smooth, round ball. Arrange the shaped rolls in a lightly greased 9×13 inch baking dish, leaving a little space between them. Cover the dish again and let the rolls rise for another 30-60 minutes, or until they look puffy and have nearly doubled again.

6. Preheat Oven and Bake: While the rolls are on their second rise, preheat your oven to 375 F (190 C). Once the rolls are fully proofed, bake them for 18-22 minutes, or until they are golden brown on top and sound hollow when tapped on the bottom.

7. Butter and Serve: As soon as you take the rolls out of the oven, brush the tops with the tablespoon of melted butter. This adds a lovely sheen and extra flavor. Let them cool slightly in the pan before serving warm.