1. 1. Activate the Yeast: In a large mixing bowl, combine the warm milk, granulated sugar, and active dry yeast. Stir gently and let it sit for 5-10 minutes until the mixture becomes foamy. This foam indicates your yeast is active and ready to work.

2. 2. Combine Wet Ingredients: Add the sourdough discard and melted butter to the yeast mixture. Stir everything together until well combined. The mixture will look a bit shaggy at this point, which is perfectly normal.

3. 3. Add Dry Ingredients: Gradually add the all-purpose flour and salt to the wet ingredients. Mix with a wooden spoon or your hands until a shaggy dough forms.

4. 4. Knead the Dough: Turn the dough out onto a lightly floured surface. Knead for 5-7 minutes until the dough is smooth, elastic, and no longer sticky. If the dough is too sticky, add a tiny bit more flour, a tablespoon at a time, but be careful not to add too much.

5. 5. First Rise (Proofing): 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 60-90 minutes, or until doubled in size.

6. 6. Shape the Buns: Gently punch down the risen dough to release the air. Divide the dough into 6-8 equal pieces (depending on your desired bun size). Shape each piece into a smooth, round ball by tucking the edges underneath. Place the shaped buns on a baking sheet lined with parchment paper, leaving some space between them.

7. 7. Second Rise and Topping: Cover the shaped buns loosely with plastic wrap or a kitchen towel and let them rise again for another 30-45 minutes, or until visibly puffy. Preheat your oven to 375 F (190 C) during the last 15 minutes of this rise. If desired, whisk the egg and brush a thin layer over the top of each bun, then sprinkle with sesame seeds.

8. 8. Bake the Buns: Bake for 15-18 minutes, or until the buns are golden brown on top and sound hollow when tapped on the bottom. Remove from the oven and transfer to a wire rack to cool completely before slicing and serving.