Measure 3 cups of bread flour into a bowl; remove 3 tablespoons of the flour and add to a saucepan with 1/2 cup milk. Cook over medium-high, whisking constantly, until the mixture becomes a thick paste, about 2 minutes. Remove from heat.

When flour paste cools to being warm but not hot to the touch, whisk together water, yeast, and sugar in a large clean bowl until sugar is dissolved. Add cooked flour mixture and whisk until well combined (a few lumps may remain). Allow to sit at room temperature until foamy, about 10 minutes.

To the foamy yeast sponge, add remaining flour and salt, and mix with hands until a shaggy dough forms. Add remaining 1 tablespoon milk and butter; combine with hands until butter is well incorporated. Transfer dough to work surface and knead until smooth, 3 to 4 minutes. Place dough in a greased bowl, cover with plastic wrap, and allow to rise at room temperature until almost tripled in volume, about 2 hours.

Punch down dough and on a lightly floured surface, roll out to an 8- x- 15-inch rectangle. Roll from one short side to the other, making an 8-inch long roll. Press down the roll, and roll out again into an 8- x- 15 inch rectangle, lightly flouring as needed to prevent sticking. Roll again from one short side to the other. Place roll seam side down in a lightly greased 9- x- 5-inch loaf pan. Cover and let rise until dough rises about an inch over the lip of the pan, about 1 hour.

Preheat oven to 350°F and adjust oven rack to the lowest position. Bake loaf, rotating pan halfway through baking, until top is well browned and bread has a hollow sound when tapped, 35 to 40 minutes. Let loaf cool in pan for 15 minutes before inverting on a wire rack to cool completely.