Step 1:In the bowl of a stand mixer, combine warm water (98-100°F) and sourdough discard. Mix quickly to incorporate. This is especially important if your discard is cold from the refrigerator—the warm water helps bring everything to the right temperature for optimal yeast activation.
Step 2:Add the sugar and instant yeast to the mixture. Wait 3-5 minutes for the yeast to activate—you'll notice a distinctive yeasty aroma and the yeast will begin to clump together or foam slightly on the surface.
Step 3:Add the egg, melted butter, and salt to the mixture. Mix until well combined, about 30 seconds on low speed.
Step 4:With the dough hook attachment running on low speed, gradually add the bread flour, reserving about a cup to add at the end. This prevents over-flouring the dough, which would make tough rolls. The perfect dough should feel tacky but not excessively sticky.
Step 5:Knead the dough with the mixer on medium-low speed for 5-7 minutes until it forms a smooth, elastic ball. If mixing by hand, knead on a lightly floured surface for 7-8 minutes until smooth and elastic.
Step 6:Turn the dough out onto a lightly floured countertop. Divide it into twelve equal pieces (about 85-90 grams each) using a bench scraper or knife.
Step 7:Shape each piece into a ball by pulling and pinching the sides upward, then roll on the counter while cupping your hand to create tension and seal the bottom. This shaping technique creates that professional bakery look and ensures even rising.
Step 8:Arrange the shaped rolls in a parchment-lined 12-inch round (or 9×13-inch rectangular) baking pan. Place them close enough that they'll touch after rising, which creates soft sides.
Step 9:Cover the rolls with a clean kitchen towel and set in a warm place to rise for about 30 minutes. The rolls should nearly double in size and touch each other when properly risen. They'll feel light and fluffy to a gentle touch.
Step 10:When the rolls have risen, preheat your oven to 375°F. (Important: If proofing your rolls in the oven with just the light on, remove them BEFORE preheating!)
Step 11:While the oven preheats, prepare a simple egg wash by beating an egg with a splash of water. Gently brush this mixture over the tops of the rolls for that beautiful golden shine.
Step 12:Bake for approximately 20 minutes until the rolls are golden brown and reach an internal temperature of 190°F if using a thermometer.
Step 13:For an extra touch of indulgence, brush the tops with additional melted butter right after baking. Allow the rolls to cool for 5-10 minutes before serving warm.