Instructions

Whisk flour, yeast, and salt together in large bowl. Whisk 6 eggs, water, and sugar together in medium bowl until sugar has dissolved. Whisk in butter until smooth. Add egg mixture to flour mixture and stir with wooden spoon until uniform mass forms and no dry flour remains, about 1 minute. Cover bowl with plastic wrap and let stand for 10 minutes.
Holding edge of dough with your fingertips, fold dough over itself by gently lifting and folding edge of dough toward middle. Turn bowl 45 degrees; fold again. Turn bowl and fold dough 6 more times (total of 8 folds). Cover with plastic and let rise for 30 minutes. Repeat folding and rising every 30 minutes, 3 more times. After fourth set of folds, cover bowl tightly with plastic and refrigerate for at least 16 hours or up to 48 hours.
Line 2 rimmed baking sheets with parchment paper. Transfer dough to well-floured counter and divide into 10 equal pieces. Working with 1 piece of dough at a time, pat dough into disk. Working around circumference of dough, fold edges of dough toward center until ball forms. Flip dough over and, without applying pressure, move your hands in small circular motions to form dough into smooth, taut round. (Tackiness of dough against counter and circular motion should work dough into smooth, even ball, but if dough sticks to your hands, lightly dust top of dough with flour.) Repeat with remaining dough.
Arrange buns on prepared sheets, 5 per sheet. Cover loosely with plastic and let rise at room temperature until almost doubled in size, 1 to 1½ hours. Thirty minutes before baking, adjust oven racks to upper-middle and lower-middle positions and heat oven to 350 degrees.
Remove plastic and brush rolls gently with remaining 1 egg beaten with salt. Bake until golden brown and internal temperature registers 190 degrees, 15 to 20 minutes, rotating and switching sheets halfway through baking. Transfer sheets to wire rack and let cool for 5 minutes. Transfer buns to wire rack. Serve warm or at room temperature.