Whisk together the lukewarm milk, sugar, and active sourdough starter in a large mixing bowl until the starter is dissolved.

Add the bread flour and salt, mixing by hand or stand mixer until a shaggy dough forms.

Knead the dough for 5 minutes, then gradually incorporate the softened butter, one tablespoon at a time, until the dough is smooth, elastic, and passes the windowpane test.

Place the dough in a lightly oiled bowl, cover, and bulk ferment at room temperature for 5 to 6 hours, performing stretch and folds every 60 minutes for the first 3 hours.

Turn the dough onto a lightly floured surface, degas gently, and shape into a tight cylinder.

Place the dough into a greased 9x5 inch loaf pan, cover, and proof for 3 to 4 hours until the dough has risen approximately 1 inch above the rim of the pan.

Preheat the oven to 375°F (190°C) and brush the top of the loaf with a beaten egg wash.

Bake for 35 to 40 minutes until the internal temperature reaches 195°F (90°C) and the crust is deep golden brown.

Remove from the pan immediately and cool completely on a wire rack for at least 2 hours before slicing.