1. Combine Wet Ingredients and Yeast: In a large mixing bowl, whisk together the warm milk, granulated sugar, and instant yeast. Let it sit for about 5 minutes until the yeast becomes foamy, indicating it’s active. If using active dry yeast, let it sit for 10 minutes until bubbly.

2. Add Sourdough and Enrichments: Stir in the sourdough discard, lightly beaten egg, 1/4 cup melted butter, and salt into the yeast mixture. Mix until well combined.

3. Incorporate Flour and Knead the Dough: Gradually add the all-purpose flour, one cup at a time, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. Turn the dough out onto a lightly floured surface and knead for 8-10 minutes, or until the dough is smooth, elastic, and no longer sticky. It should spring back when gently poked.

4. First Rise: Lightly grease a clean 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 60-90 minutes, or until doubled in size.

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 12-16 equal pieces, depending on your desired roll size. Shape each piece into a smooth, round ball by pulling the edges underneath and pinching them together at the bottom.

6. Second Rise: Arrange the shaped rolls in a lightly greased 9×13 inch baking dish, leaving a little space between them. Cover the dish loosely with plastic wrap or a kitchen towel and let the rolls rise again in a warm place for 30-45 minutes, or until they look puffy and almost doubled in size.

7. Bake to Golden Perfection: Preheat your oven to 375 F (190 C). Once the rolls have completed their second rise, remove the cover. Bake for 18-22 minutes, or until the tops are golden brown and the rolls sound hollow when tapped on the bottom.

8. Final Touch: As soon as the rolls come out of the oven, brush the tops with the remaining 2 tablespoons of melted butter. This adds a beautiful sheen and extra richness. Serve warm and enjoy!