1. 1. Activate the Yeast and Combine Wet Ingredients: In a large mixing bowl, combine the warm milk and granulated sugar. Sprinkle the active dry yeast over the top and let it sit for 5-10 minutes until it becomes foamy. This foam indicates your yeast is active. Once foamy, stir in the sourdough discard, beaten egg, and melted butter until well combined. The mixture will look slightly cloudy.

2. 2. Mix the Dough: In a separate bowl, whisk together the all-purpose flour and salt. Gradually add the dry ingredients to the wet ingredients, mixing with a wooden spoon or a stand mixer with a dough hook on low speed until a shaggy dough forms. Continue to mix for about 5-7 minutes until the dough comes together, is smooth, and pulls away from the sides of the bowl. It should be soft and slightly tacky, but not sticky.

3. 3. First Rise: Lightly grease a clean bowl with a little oil. Transfer the dough to the greased bowl, turning it once to coat the entire surface. Cover the bowl tightly with plastic wrap or a clean kitchen towel. Let the dough rise in a warm place for 1 hour 30 minutes to 2 hours, or until it has doubled in size. You’ll know it’s ready when it looks significantly larger and feels airy.

4. 4. Shape the Buns: Gently punch down the risen dough to release the air. Turn it out onto a lightly floured surface. Divide the dough into 12 equal pieces. For each piece, gently pull the edges underneath and pinch them together to form a smooth ball. Place the shaped buns into a greased 9×13-inch baking dish, leaving a little space between each bun. They will expand during the second rise.

5. 5. Second Rise: Cover the baking dish loosely with plastic wrap or a kitchen towel. Let the buns rise in a warm place for another 45 minutes to 1 hour, or until they look noticeably puffy and have nearly doubled in size. They should be touching each other slightly.

6. 6. Bake the Buns: Preheat your oven to 375 F (190 C) during the last 15 minutes of the second rise. If desired, gently brush the tops of the risen buns with 1 tablespoon of milk for a golden finish. Bake for 18-22 minutes, or until the tops are golden brown and the buns sound hollow when tapped on the bottom.

7. 7. Cool and Serve: Once baked, remove the buns from the oven and let them cool in the baking dish for 5-10 minutes before transferring them to a wire rack to cool completely. This helps them set up and prevents them from becoming soggy on the bottom.