Mix 3 1/2 cups of the flour, the yeast, and salt together in a standing mixer fitted with the dough hook.
With the mixer on low speed, add the milk mixture and mix until the dough comes together, about 1 minute.
Increase speed to medium-low and knead until the dough is smmooth and elastic, about 10 minutes. (If after 5 minutes, more flour is needed, add the remaining 1/4 cup of flour, 1 tablespoon at a time, until the dough cleas the side of the bowl but sticks to the bottom.).
Turn the dough onto a clean counter and knead by hand to form a smooth, round ball, aout 1 minute. Place the dough in a lightly oiled bowl and wrap tightly with palctic wrap. Let rise in a warm place until doubled in size, 1 to 1 1/2 hours. **see variation for proofing instructions).
Turn the dough out onto a lightly floured counter and gently press it into a 9-inch square. Roll the dough into a tight cylinder and pinch the seam closed. Place the loaf seam-side down in a 9-inch loaf pan, wrap tightly in plastic wrap, and let rise in a warm place until it has nearly doubled in size and springs back slowl when indented with a finger, 1 1/2 hours.
Adjust an oven rack to the middle position and heat the oven to 350 degrees. Bring a kettle of water to boil. Gently brush the loaf with the remaining 1 tablespoon butter. Set the loaf pan on the oven rack and place an empty metal loaf pan next to it. Fill the empty pan about half full with the boiling water. Bake until golden and the center of the bread registers 200 degrees on an instant-read thermometer, 40-50 minutes. Flip the bread out onto a wire rack and let cool to room temperature before slicing, about 2 hours.