1. 1. Combine Wet Ingredients: In a large mixing bowl, whisk together your active sourdough starter, warm milk, granulated sugar, 1/4 cup melted butter, and the egg until well combined. The mixture should look slightly milky and uniform.

2. 2. Add Dry Ingredients: Gradually add the salt and 3 1/2 cups of the all-purpose flour to the wet mixture. Mix with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. If the dough is too sticky, add the remaining 1/2 cup of flour, a tablespoon at a time, until it pulls away from the sides of the bowl.

3. 3. Knead the Dough: Turn the dough out onto a lightly floured surface and knead for 5-7 minutes until it becomes smooth and elastic. It should spring back slowly when poked. Alternatively, if using a stand mixer, knead with the dough hook for 5-6 minutes on medium speed.

4. 4. First Rise (Bulk Fermentation): Place the kneaded dough in a lightly oiled 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 2-3 hours, or until it has nearly doubled in size. The dough should look puffy and soft.

5. 5. Shape the Rolls: Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface and divide it into 12-15 equal pieces. Roll each piece into a smooth ball. Arrange the dough balls snugly in a greased 9×13 inch baking dish.

6. 6. Second Rise: Cover the baking dish loosely with plastic wrap or a clean kitchen towel and let the rolls rise again in a warm place for 30-45 minutes, or until they look visibly puffy and are touching each other. They should look light and airy.

7. 7. Bake the Rolls: Preheat your oven to 375 F (190 C). Once preheated, bake the rolls for 20-25 minutes, or until they are golden brown on top and cooked through. The internal temperature should reach about 200 F (93 C).

8. 8. Brush with Butter: 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 in the pan before serving.