Warm water, milk, and sugar to 100–110°F (38–43°C).
Stir in active dry yeast.
Let sit for 5–10 minutes until frothy.
Add flour, sourdough discard, and yeast mixture to the bowl of a stand mixer fitted with a dough hook.
Mix on low speed for 5 minutes.
Add softened butter and salt.
Continue mixing for another 5 minutes until smooth and elastic.
Cover the bowl.
Allow dough to rise until doubled in size, about 45–90 minutes.
Line a 9×5-inch loaf pan with parchment paper and lightly grease.
Transfer dough to a clean work surface.
Stretch into a rectangle approximately twice the length of the loaf pan.
Fold in half widthwise.
Roll tightly into a loaf shape.
Place seam-side down into the prepared pan.
Cover and allow dough to rise until about 1 inch above the rim of the pan, approximately 45–90 minutes.
Preheat oven to 350°F (177°C).
Bake for 33 minutes until golden brown.
Cool in pan for 30 minutes.
Remove from pan and cool completely on a wire rack before slicing.
