01 - Combine warm milk and sugar in a large mixing bowl. Sprinkle instant yeast over the surface and let stand 3 to 5 minutes until mixture becomes foamy and bubbly.
02 - Add sourdough discard, melted butter, egg, and salt to the yeast mixture. Whisk thoroughly until fully incorporated and smooth.
03 - Gradually add flour, one cup at a time, mixing with a wooden spoon or dough hook after each addition. Continue adding flour until a soft, slightly tacky dough forms that pulls away from the bowl sides.
04 - Turn dough onto a lightly floured surface. Knead by hand for 7 to 8 minutes, pushing dough away with the heel of your hand and folding it back toward you, until smooth, elastic, and springs back when pressed.
05 - Place dough in a lightly greased bowl, turning once to coat all surfaces. Cover with plastic wrap or a clean kitchen towel. Let rise in a warm, draft-free area until doubled in bulk, approximately 1 to 1 ½ hours.
06 - Punch down risen dough to release air. Divide into 8 equal portions using a bench scraper or sharp knife. Roll each portion into a smooth 6-inch log, tapering the ends slightly.
07 - Arrange shaped buns on a parchment-lined baking sheet, spacing 2 inches apart. Cover loosely and let rise until puffy and visibly increased in size, 30 to 45 minutes.
08 - Position oven rack in the center position. Preheat oven to 375°F.
09 - Brush risen buns lightly with milk. Sprinkle with sesame seeds, poppy seeds, or everything seasoning if desired. Bake for 18 to 20 minutes until deep golden brown and internal temperature reaches 190°F.
10 - Remove buns from oven immediately. Brush tops with melted butter for a softer crust. Transfer to a wire rack and cool completely before slicing to prevent crumbling.