Place the all-purpose and bread flours in a large mixing bowl and whisk to combine.
Add the water, yeast, sugar, salt, and eggs, and mix together on medium-low speed until combined (approx. 7 minutes), stopping to scrape the bottom and sides of the bowl with a silicone spatula.
While continuing to mix on low speed, add the butter a tablespoon at a time, allowing each addition to fully incorporate before adding the next.
When all the butter has been added, knead the dough on low speed for 10 minutes, then increase the speed to medium and knead for an additional 15 minutes.
Allow the dough to chill in a greased, covered bowl overnight in the refrigerator .
Divide the dough in half, then divide each half into 8 equal portions.
Roll each portion in a tight, smooth ball, and line the dough balls up in 2 staggered rows of 4, in each of 2 greased loaf pans (see video below).
Cover the loaf pans with greased plastic wrap, then allow them to rise in a warm place for 4 to 5 hours.
Preheat the oven to 350 degrees F and brush the unbaked loaves with egg wash.
Bake the loaves until puffed, deeply golden, and set (approx. 30 to 40 minutes).
Cool for 30 minutes in the pans, then transfer them to a wire rack to cool completely.