In a small pan, heat the water and butter together just until butter is melted.
Pour warm butter water into a large mixing bowl, along with the milk.
Add the yeast and whisk to incorporate.
Add sugar, salt, eggs, and 2.5 cups of the flour. Mix to form a slightly sticky dough.
Put the remaining 1/2 cup of flour onto kneading surface - it works well to spread it into a circle just larger than the ball of dough. Turn the dough onto the floured surface, and knead until all flour is incorporated, and dough is smooth and elastic.
Form into a loaf, and place in a well-greased (or parchment lined) bread pan. Let rise for 50 minutes, or until double.
Meanwhile, pre-heat oven to 400°, making sure the center rack position is available for the bread when the time comes.
When bread has risen, place in the middle of the center rack, and bake for 22-25 minutes, until richly brown. Loaf will sound hollow if lightly rapped.
Remove from oven. For a really perfect loaf, let bread rest for just 5-10 minutes, then carefully turn out of the pan to finish cooling the rest of the way. This gives an improved texture to the lower crusts.