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 foam indicates your yeast is active and ready to work.

2. Combine Wet Ingredients: To the foamy yeast mixture, add the sourdough discard, 1/4 cup melted butter, and the egg. Whisk everything together until well combined. The mixture will look slightly cloudy.

3. Add Dry Ingredients: Gradually add the salt and 3 1/2 cups of all-purpose flour to the wet ingredients. Mix with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms. If the dough is too sticky, add the remaining 1/2 cup of flour, a little at a time, until it 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 until it becomes smooth and elastic. Alternatively, if using a stand mixer, knead with the dough hook for 5-7 minutes on medium-low speed. The dough should spring back 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. Cover the bowl with plastic wrap or a clean kitchen towel and let it rise in a warm place for 1.5 to 2 hours, 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 12-16 equal pieces, depending on your desired roll size. Roll each piece into a smooth, tight ball.

7. Second Rise and Bake: Arrange the shaped rolls in a lightly greased 9×13 inch baking dish, leaving a little space between each. Cover again and let them rise for another 30-45 minutes, or until visibly puffy. Preheat your oven to 375 F (190 C) during the last 15 minutes of the second rise.

8. Bake and Finish: Bake the rolls for 15-20 minutes, or until golden brown on top. Once out of the oven, immediately brush the tops with the remaining 2 tablespoons of melted butter. This adds flavor and a beautiful shine. Let them cool slightly before serving.