Pour the yeast, water and milk in the bowl of a stand mixer and, using a wooden spoon, stir until the yeast is dissolved (about 5 minutes). Add in the flour and salt, and fit the mixer with the dough hook attachment. Using the plastic covering or a kitchen towel, cover the mixer. Turn the mixer on and off a few short pulses (just to dampen the flour), remove the towel and increase the mixer speed to medium-low and mix for a minute or two, or just until the flour is moistened.
Scrape the sides and bottom of the bowl with a rubber spatula, set the mixer to low and add the eggs one at a time, followed by the sugar. Increase the speed to medium and mix for about 3 minutes, or until the dough forms a ball.
Reduce the speed to low and add the butter in 2-tablespoon-size chunks, beating until each piece is almost incorporated before adding the next. You’ll have a dough that is very soft, almost like a cake batter. Increase the speed to medium-high and continue to beat until the dough pulls away from the sides of the bowl, for about 10 minutes.
Transfer the dough to a clean bowl (lightly greased with butter), cover with plastic wrap and leave at room temperature until nearly doubled in size, for about 40 to 60 minutes, depending upon the warmth of your room.
Deflate the dough by lifting it up around the edges and letting it fall with a slap to the bowl. Cover the bowl with the plastic wrap and put it in the refrigerator. Slap the dough down in the bowl every 30 minutes until it stops rising, for about 2 hours, then leave the uncovered dough in the refrigerator to chill overnight.
The next morning, butter and flour two 8 1/2-x-4 1/2-inch pans. Remove the dough from the refrigerator and divide it into 2 equal pieces. (I waited about 15-30 minutes after removing the dough from the fridge so the dough was easier to work with). Cut each piece of the dough into 4 equal pieces and roll each piece into a log about 3 1/2 inches long. Arrange 4 logs crosswise in the bottom of each pan. Place the pans on a baking sheet and cover the pans lightly with wax paper and leave the loaves at room temperature until the dough almost fills the pans, for about 1 to 2 hours.
Center a rack in the oven and preheat the oven to 400 degrees F. (Note: Nancy baked her loaves at 390. You know your oven best).
To Make the egg wash: Beat the egg with the water. Using a pastry brush, gently brush the tops of the loaves with the glaze.
Bake the loaves until they are well risen and deeply golden, about 30 to 35 minutes. Transfer the pans to racks to cool for 15 minutes, then run a knife around the sides of the pans and turn the loaves out onto the racks. Invert again and cool for at least 1 hour before serving.