1. Activate the Yeast: In a large mixing bowl, combine the warm milk, granulated sugar, and active dry yeast. Stir gently and let it sit for 5-10 minutes until the mixture becomes foamy. This indicates your yeast is active and ready to go.

2. Combine Wet Ingredients: To the foamy yeast mixture, add the active sourdough starter, the room temperature egg, 1/4 cup of melted and slightly cooled butter, and the salt. Whisk everything together until well combined.

3. Mix in the Flour: Gradually add 3 1/2 cups of all-purpose flour to the wet ingredients, mixing with a wooden spoon or a stand mixer with a dough hook attachment until a shaggy dough forms. If the dough is too sticky, add the remaining flour a little at a time until it comes together and pulls away from the sides of the bowl.

4. Knead the Dough: Turn the dough out onto a lightly floured surface and knead for 5-7 minutes, or use a stand mixer with a dough hook for 3-5 minutes, until the dough is smooth and elastic. It should spring back slowly when gently poked.

5. First Rise: Lightly grease a clean bowl with a little oil. Place the dough in the bowl, turning it once to coat the top. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1 hour to 1 hour 30 minutes, or until doubled in size.

6. 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 equal pieces. Roll each piece into a smooth, round ball. Arrange the rolls in a greased 9×13-inch baking dish, leaving a little space between them.

7. 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 puffy and have nearly doubled in size. Towards the end of this rise, preheat your oven to 375 F (190 C).

8. Bake and Butter: Bake the rolls in the preheated oven for 18-22 minutes, or until they are golden brown on top. Immediately after removing them from the oven, brush the tops with the remaining 2 tablespoons of melted butter. This creates that beautiful golden shine and adds extra flavor.