1. Activate the Starter and Combine Wet Ingredients: In a large mixing bowl, combine your active sourdough starter, warm milk, granulated sugar, melted butter, and the egg. Whisk these ingredients together until they are well combined and the sugar has dissolved. If you’re using instant yeast, sprinkle it over this mixture and let it sit for 5 minutes until foamy.

2. Mix in Dry Ingredients to Form Dough: Add the salt and 3 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. Gradually add the remaining 1/2 cup of flour, a little at a time, until the dough comes together and is no longer excessively sticky. It should be soft and slightly tacky, but not sticking to your hands or the sides of the bowl.

3. Knead the Dough for Development: Turn the dough out onto a lightly floured surface. Knead for 8-10 minutes until the dough is smooth, elastic, and passes the “windowpane test” (you can stretch a small piece thin enough to see light through it without tearing). If using a stand mixer, knead with the dough hook on medium speed for 6-8 minutes.

4. First Rise (Bulk Fermentation): 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 damp kitchen towel. Let the dough rise in a warm place for 4-8 hours, or until it has doubled in size. Alternatively, for a longer, colder ferment that develops more flavor, you can place it in the refrigerator overnight (8-12 hours).

5. Shape the Dinner 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. Roll each piece into a smooth, tight ball. Arrange the shaped rolls in a lightly 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 towel. Let the rolls rise in a warm place for 1-2 hours, or until they look puffy and have nearly doubled in size. They should be soft and spring back slowly when gently poked.

7. Bake Until Golden Brown: Preheat your oven to 375 F (190 C). Once preheated, remove the cover from the rolls and place the baking dish in the oven. Bake for 18-22 minutes, or until the tops are golden brown and the rolls sound hollow when tapped on the bottom.

8. Finish with Butter and Serve: As soon as the rolls come out of the oven, brush the tops with the 2 tablespoons of melted butter. This adds flavor, shine, and helps keep them soft. Let them cool slightly in the pan before serving warm.