In a large bowl (or the bowl of a stand mixer), combine the warm milk, granulated sugar, and active dry yeast. Stir gently and let it sit for 5-10 minutes until foamy, indicating the yeast is active.

Add the sourdough discard to the yeast mixture and stir until well combined.

Add the all-purpose flour and fine sea salt to the wet ingredients. Mix with a spoon or the dough hook attachment of your stand mixer on low speed until a shaggy dough forms. Cover the bowl and let it rest for 10 minutes (autolyse) to allow the flour to hydrate.

Add the softened unsalted butter. Knead the dough for 8-10 minutes by hand or with a stand mixer on medium-low speed, until the dough is smooth, elastic, and passes the windowpane test. It should be slightly tacky but not sticky.

Lightly grease a clean large bowl. Form the dough into a ball and place it in the greased bowl, turning once to coat. Cover the bowl tightly with plastic wrap or a clean kitchen towel.

Let the dough rise in a warm place for 1.5 to 2.5 hours, or until it has nearly doubled in size. The exact time will depend on your room temperature and the activity of your discard.

Lightly grease a 9x5 inch loaf pan. Gently punch down the risen dough to deflate it. Turn the dough out onto a lightly floured surface.

Shape the dough into a log by gently flattening it into a rectangle (about 8-9 inches wide). Fold the top edge down to the center, press to seal. Then fold the bottom edge up to the center, press to seal. Finally, fold the dough in half lengthwise, pinching the seam tightly to create tension on the top. Roll the log slightly to ensure it fits the length of your loaf pan.

Place the shaped dough seam-side down into the prepared loaf pan.

Cover the loaf pan loosely with plastic wrap or a clean kitchen towel. Let it rise in a warm place for another 45-90 minutes, or until the dough has risen about 1 inch above the rim of the pan and looks puffy.

Preheat your oven to 375°F (190°C) about 15-20 minutes before the end of the second rise.

If desired, prepare the egg wash: whisk together the egg and milk/water in a small bowl. Gently brush the top of the risen dough with the egg wash for a golden, shiny crust.

Bake for 30-35 minutes, or until the top is golden brown and the internal temperature reaches 200-210°F (93-99°C).

Remove the loaf from the oven and immediately turn it out onto a wire rack to cool completely. This is crucial to prevent a soggy bottom and ensure proper texture.

Slice and enjoy once fully cooled (at least 1-2 hours).