In the bowl of a stand mixer, fitted with the dough hook, combine flour and yeast. Add water and 4 of the eggs. Mix on low speed until no dry flour remains. Scrape down frequently. Cover bowl with plastic wrap or a tea towel and let sit for 15 minutes.
Add sugar and salt to the bowl and knead on medium speed until incorporated. With the mixer running, add butter, one piece at a time, mixing after each addition until each piece is incorporated. Scrape down the bowl, then knead for 10-15 minutes until the dough is elastic and pulls away from the side of the bowl.
Transfer dough to greased bowl and cover with greased plastic wrap. Let rise at room temperature until doubled in size, about 1 hour.
Grease two 8x4 pans. Punch down dough in the bowl, turn out onto floured work surface and divide the dough into 16 equal pieces. Roll into balls and place eight balls in each baking pan. Cover pans with greased plastic wrap and let dough rise until doubled in size, about 45 min.
Preheat oven to 350 degrees F. Lightly beat remaining egg and brush over loaves (you don’t need to use all of it). Bake loaves for 30-35 minutes until loaves are golden brown and register 205 to 210 degrees in center, rotating pans halfway through baking.
Let loaves cool for 15 minutes on a cooling rack, then remove loaves from pans and let cool completely.