01 - Combine warm milk, sugar, and instant yeast in a large mixing bowl. Let the mixture sit for 3 to 5 minutes until it becomes bubbly and foamy, indicating the yeast is active.
02 - Add sourdough discard, melted butter, egg, and salt to the yeast mixture. Stir thoroughly until all wet ingredients are fully incorporated.
03 - Gradually add flour, one cup at a time, mixing after each addition. Continue adding flour until a soft, slightly tacky dough forms. You may not need the full 4 cups depending on humidity.
04 - Turn the dough onto a lightly floured surface. Knead for 7 to 8 minutes, working the dough until it becomes smooth, elastic, and springs back when pressed.
05 - Place the dough in a lightly greased bowl, turning once to coat all sides. Cover with plastic wrap or a clean towel and let rise in a warm, draft-free area until doubled in size, approximately 1 to 1.5 hours.
06 - Punch down the risen dough to release air bubbles. Divide into 8 equal portions and roll each into a smooth log about 6 inches long, tapering the ends slightly for an authentic bun shape.
07 - Arrange shaped buns on a parchment-lined baking sheet, leaving 2 inches of space between each to allow for expansion. Cover and let rise until puffy and noticeably expanded, 30 to 45 minutes.
08 - Preheat your oven to 375°F while the buns complete their second rise.
09 - Brush the risen buns with milk and sprinkle with sesame seeds, poppy seeds, or everything seasoning if desired. Bake for 18 to 20 minutes until golden brown on top.
10 - Remove buns from the oven and immediately brush with melted butter for a softer, more tender crust. Allow to cool completely on the baking sheet before slicing and serving.