Microwave butter and ½ cup of the milk on HIGH in 10 to 15 second intervals until butter is melted, about 1 minute.

Add butter mixture to the bowl of a stand mixer fitted with a dough hook attachment; stir in salt, sugar, and remaining 1 cup milk.

Add preferment, yeast, and 3 ½ cups of the flour; beat on low speed just until combined, about 30 seconds, stopping to scrape down sides as needed.

Increase speed to medium-low and beat until a soft, somewhat sticky, elastic dough forms, 8 to 12 minutes, stopping to scrape down sides as needed; add up to remaining ½ cup flour, 1 tablespoon at a time, as needed if dough is too wet.

Transfer dough to a large bowl; cover and let stand in a warm place (75°F) until tripled in size, about 2 ½ to 3 hours.

Uncover dough. Punch down and fold by reaching a very lightly floured hand under the dough; gently pull dough up then fold toward center, repeating this motion 3 more times around the bowl.

Cover and let stand in a warm place (75°F) until tripled again in size, about 1 ½ to 2 hours.

Butter a 9- x 5-inch loaf pan.

Punch dough down and shape into a 12- x 9-inch rectangle on a very lightly floured surface; thoroughly degas dough, pressing out any large air bubbles.

Starting at a short end of dough rectangle, fold into thirds, like a letter. Pinch seam to seal.

Place seam side down in prepared loaf pan, gently evening out dough and tucking in ends if needed.

Cover with a clean dish towel and let rise in a warm place (75°F) for 1 hour, until loaf is puffy and part of its rounded top has risen up to or above the top of the pan.

About 30 minutes before baking, preheat oven to 425°F with rack in the middle of the oven.

Bake loaf until top is puffed and a rich brown color, about 20 minutes.

Cover loaf loosely with foil, reduce heat to 375°F and bake for 20 minutes longer.

Immediately turn the loaf out of pan and onto a wire rack to cool completely, about 2 to 3 hours.

Whisk ½ cup tepid water (105* - 110*) with ½ tsp active dry yeast and 1 cup all purpose flower in a large bowl. Cover with plastic wrap and let sit for several hours to overnight in a cool room. The Preferment will rise and form big bubbles and then sink down, at which time it is ready for use. You can also cover it and refrigerate it for a couple of days.