01 - Combine warm milk, sugar, and instant yeast in a large mixing bowl. Let stand 3 to 5 minutes until mixture becomes foamy and bubbly, indicating yeast activation.
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. Stop adding flour when a soft, slightly tacky dough forms that pulls away from bowl sides.
04 - Turn dough onto a lightly floured surface. Knead by hand for 7 to 8 minutes, or use stand mixer with dough hook for 5 minutes, until smooth, elastic, and passes the windowpane test.
05 - Place dough in a lightly greased bowl, turning to coat all surfaces. Cover with plastic wrap or clean towel. Let rise in warm, draft-free area until doubled, approximately 1 to 1.5 hours.
06 - Punch down dough to release air. Divide into 8 equal portions. Roll each piece into a smooth 6-inch log, tapering ends slightly and keeping surface taut.
07 - Arrange shaped logs on parchment-lined baking sheet, leaving 2 inches between each. Cover loosely and let rise 30 to 45 minutes until puffy and slightly increased in size.
08 - Preheat oven to 375°F with rack positioned in center.
09 - Brush risen buns lightly with milk. Sprinkle with seeds if using. Bake 18 to 20 minutes until deep golden brown and internal temperature reaches 190°F.
10 - Remove immediately from oven. Brush tops with melted butter for softer crust. Transfer to wire rack. Cool completely before slicing to prevent soggy texture.