In a small bow, dissolve the yeast in the milk. Blend in 1 cup of the flour to form a shaggy ball. Cover and let rest at room temperature 2 hours.
Place 2 cups of the remaining flour in a large bowl and mix in 4 of the eggs, one at a time, stirring until incorporated. Add the water, sugar, and salt. Mix to form a thick batter.
On a work surface, using a dough scraper (not your hands), work the butter until soft and pliable, but not melted. Blend the softened butter into the batter. Add the remaining eggs and beat until thick.
Stir the rest of the flour in to the batter, 1/2 cup at a time, until dough is soft and elastic. Transfer dough to a work surface.
Press the dough into a flat oval and place the starter in the center. Fold the edges of the dough over the starter and knead to incorporate. Continue kneading until both doughs have completely blended. The dough should be soft and tacky, and will stiffen when chilled.
Transfer the dough to a greased bowl, cover, and let rest at room temperature until doubled.
Punch down the dough, flip, cover, and refrigerate for at least 2 hours, or overnight.
If refrigerating for longer than 2 hours, the dough will need longer to rise before being baked.
The dough was incredibly sticky and could only be handled with a bench scraper, but was much more firm after refrigerating (which I did overnight). It still required floured hands to form before baking, but was not unmanageable. The flavor of this bread is very nice, which I attribute to the slow fermentation during the cold rise.
Made this before Christmas for use in the bread pudding.