1. 1. Combine Wet Ingredients: In a large mixing bowl, whisk together the sourdough discard, warm milk, granulated sugar, room temperature egg, and melted butter until well combined. The mixture should look slightly milky and smooth.

2. 2. Add Dry Ingredients: In a separate bowl, whisk together the all-purpose flour, salt, and instant yeast. Gradually add the dry ingredients to the wet ingredients, mixing with a wooden spoon or a stand mixer with a dough hook until a shaggy dough forms.

3. 3. 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 on medium-low speed for 5-7 minutes. The dough should be soft and slightly tacky, but not sticky.

4. 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 1 to 1 1/2 hours, or until doubled in size.

5. 5. 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 equal pieces. Roll each piece into a smooth ball. Arrange the dough balls in a greased 9×13 inch baking pan, leaving a little space between them.

6. 6. Second Rise and Preheat Oven: Cover the pan 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 have nearly doubled in size. Towards the end of the second rise, preheat your oven to 375 F (190 C).

7. 7. Egg Wash and Bake: If desired, gently brush the tops of the risen rolls with the egg wash (1 beaten egg mixed with 1 tablespoon water). This will give them a beautiful golden-brown crust. Bake for 15-20 minutes, or until the rolls are golden brown on top and sound hollow when tapped on the bottom.

8. 8. Cooling: Once baked, remove the pan from the oven and let the rolls cool in the pan for 5-10 minutes before transferring them to a wire rack to cool completely.