In the bowl of a stand mixer, combine the sourdough starter, water, milk, butter, and honey. Mix briefly until combined.
Add the flour and salt. Mix on low speed until a dough forms.
Knead on medium-low speed with the dough hook for 6 to 8 minutes, until the dough is smooth and elastic. It should pull away from the sides of the bowl and feel soft and slightly tacky.
Cover with plastic wrap and put it in a warm space for its first rise (not too warm, between 70-75 degrees F) until puffy and almost doubled in size (4-8 hours).
Turn the dough out onto a lightly floured surface. Press it into a rectangle, then roll it up tightly into a loaf. Pinch the seam closed.
Place the dough seam side down into a greased loaf pan. Cover and let rise until the dough has risen an inch above the top edge of the pan, about 2 hours.
Bake at 375°F for 25 to 30 minutes, or until the center reads 195 degrees F.
Remove from the pan and let cool. Brush the top with butter while warm if you want a softer crust.
Cool completely before slicing.