Note: A heavy stand mixer is needed for this recipe.
Combine 2 cups flour, undissolved yeast, water and eggs in a large bowl. Beat 1 minute at high speed of electric mixer until smooth. Cover and let rest 45 minutes.
Add remaining flour, sugar and salt; beat on low speed to incorporate. Beat 8 minutes at high speed, scraping bowl occasionally. Cut 1 stick butter in half lengthwise, then slice into 1/2 inch slices. Beat in butter using medium speed of mixer, a few bits at a time, until fully incorporated. Cover bowl and let dough rise in refrigerator for a minimum 4 hours or overnight.
Divide dough into 8 to 10 equal portions; shape into balls. Place on greased OR parchment paper lined baking sheets (4 to 5 buns per sheet). Flatten with palm of hand to about 3/4-inch in height. Cover and let rise until doubled in size, about 30 to 45 minutes.
Mix egg yolk and water until thoroughly combined. Brush over tops of buns.
Bake in preheated 350ºF oven for 20 to 25 minutes or until done. Remove from pan; cool on wire rack.
Note: Buns will have some cracks on the surface. This is normal.