Step 1: Ensure your sourdough starter is active and bubbly. If refreshing, combine 1 tablespoon of starter with ⅓ cup + 1 tablespoon (50g) all-purpose flour and 3 ½ tablespoons (50g) warm water, and let it activate for 4-8 hours until doubled.
Step 2: In a large mixing bowl, whisk together the warm milk, sugar, and 2 tablespoons of melted butter. Add the active sourdough starter and stir until mostly combined.
Step 3: Gradually add 3 ½ cups (420g) all-purpose flour and the salt. Mix with a spoon or your hands until a shaggy dough forms. Turn the dough out onto a lightly floured surface.
Step 4: Knead the dough for 8-10 minutes until it becomes smooth, elastic, and passes the windowpane test. If using a stand mixer, knead with a dough hook on medium speed for 6-8 minutes.
Step 5: Place the dough in a lightly oiled bowl, turning once to coat. Cover with plastic wrap or a damp towel and let it bulk ferment at room temperature (70-75°F) for 8-12 hours, or until it has noticeably increased in volume and is bubbly.
Step 6: Gently punch down the dough and turn it out onto a lightly floured surface. Divide the dough into 12 equal pieces (approximately 60-65g each). Shape each piece into a tight, smooth ball.
Step 7: Arrange the shaped rolls in a greased 9x13 inch baking dish or a 9-inch round cake pan, leaving a little space between each roll. Cover loosely and let them proof at room temperature for another 2-3 hours, or until they look puffy and have nearly doubled in size.
Step 8: Preheat your oven to 375°F (190°C). Bake the rolls for 20-25 minutes, or until they are golden brown on top and cooked through.
Step 9: As soon as the rolls come out of the oven, brush them with the remaining 1 tablespoon of melted unsalted butter. This adds flavor and gives them a beautiful shine.
Step 10: Serve warm and enjoy your incredibly soft sourdough dinner rolls!