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

2. Add Dry Ingredients: Gradually add the melted and cooled butter, salt, and 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.

3. Knead the Dough: Slowly add the remaining 1 cup of flour, a little at a time, until the dough comes together and is no longer sticky. Transfer the dough to a lightly floured surface and knead for 8-10 minutes, or use a stand mixer with a dough hook on medium speed for 6-8 minutes, until the dough is smooth and elastic. It should spring back when gently poked.

4. First Rise (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 and let it rise in a warm place for 2-3 hours, or until doubled in size. The exact time will depend on the warmth of your kitchen and the activity of your starter.

5. Shape the Rolls: Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface. Divide the dough into 12 equal pieces. Roll each piece into a smooth, tight ball. Arrange the dough balls in a greased 9×13 inch baking dish, leaving a little space between them.

6. Second Rise (Proofing): Cover the baking dish loosely with plastic wrap or a damp kitchen towel. Let the rolls rise again in a warm place for 30-45 minutes, or until they look puffy and have nearly doubled in size.

7. Bake the Rolls: Preheat your oven to 375 F (190 C). Once the rolls have risen, remove the cover and bake for 18-22 minutes, or until they are golden brown on top and sound hollow when tapped.

8. Finish with Butter: As soon as the rolls come out of the oven, brush them generously with the remaining 1 tablespoon of melted butter. This adds a beautiful sheen and extra richness. Serve warm.