In the bowl of a stand mixer, combine the water, honey, butter, eggs, and salt.
Add 4 ½ cups flour and combine. Let it rest for 15 minutes.
Add the yeast and remaining flour, if needed. Add a half cup at a time, watching to see when it starts to pull away from the sides of the bowl. Do not add anymore flour once it starts doing this.
Knead until the dough is smooth and you reach windowpane. The dough should be somewhat sticky.
Place in a bowl and cover to rise in a warm spot until doubled, about 35-45 minutes.
Once risen, turn out on an oiled surface. Divide the dough in half, then divide each half into 3 pieces.
Roll the 3 pieces into logs about 15 inches long.
Line a baking sheet with parchment paper and place the pieces of dough on it. Attach the three strands together at one end, then braid the log and pinch the 3 ends together. Repeat with the other half of the dough to make 2 braided loaves.
Cover and allow to rise until puffy, 45 minutes to an hour.
Preheat the oven to 350 degrees F.
Once risen, whisk an egg with a teaspoon of water and brush over each loaf.
Bake for 26-32 minutes, until they are browned and reach an internal temperature of 190 degrees F.