Combine 2 1/2 cups (12.5 oz) of the flour, sugar, salt and yeast in the bowl of a stand mixer.
Add butter, warm milk, water and stir well, then add 2 tablespoons of the egg. Mix well to form a soft dough. You can do this with the paddle attachment or by hand. I do this part by hand.
Put the dough on the stand mixer and begin kneading with the dough hook. If dough does not clear the sides of the bowl, add remaining flour a tablespoon at a time until it does. Continue kneading with stand mixer for about 8 minutes.
Place dough in a large bowl coated with olive oil or cooking spray, turning to coat top.
Cover and let rise in a warm place for 1 hour or until doubled in size.
Add the walnuts and rosemary to the risen dough and punch it down, working the rosemary and walnuts into the dough.
Shape the dough into a ball on a parchment lined baking sheet. Cover with an inverted mixing bowl and let rise for about 30 minutes.
Meanwhile, preheat oven to 400°.
Add 1/2 tablespoon of milk to the remaining egg, stirring with a whisk; brush over loaf.
Make 3 diagonal cuts 1/4-inch deep across top of each loaf using a sharp knife or razor blade.
Place loaf in oven.
Immediately reduce oven temperature to 375°, and bake 40-45 minutes or until bottom sounds hollow when tapped. Let stand 20 minutes before slicing. Also, after about 30 minutes you'll probably want to shield the loaf with foil.