Instructions

for the dough

Whisk 3⅔ cups (20⅛ ounces) bread flour and 1 tablespoon instant or rapid-rise yeast together in bowl of stand mixer. Whisk 1¼ cups room temperature water and 2 room temperature large eggs in 4-cup liquid measuring cup until combined. Using dough hook on low speed, add water mixture to flour mixture and mix until cohesive dough starts to form and no dry flour remains, about 2 minutes, scraping down bowl as needed. Let rest for 15 minutes.
Add ¼ cup (1¾ ounces) granulated sugar and 2 teaspoons table salt to dough and knead on medium-low speed until incorporated, about 30 seconds. Increase speed to medium and, with mixer running, add 13 tablespoons unsalted butter, cut into 13 pieces and softened, 1 piece at a time, allowing each piece to incorporate before adding next, 4 to 6 minutes total, scraping down bowl and dough hook as needed. Continue to knead until dough is elastic and pulls away cleanly from sides of bowl, about 10 minutes longer.
Transfer dough to greased large bowl, cover with greased plastic wrap, and let dough rise until doubled in volume, about 1 hour.

for the chocolate sugar crust

While dough rises, in clean, dry mixer bowl, combine 1 cup (4 ounces) confectioners’ sugar, ⅔ cup (3⅔ ounces) bread flour, 3 tablespoons unsweetened cocoa powder, 10 tablespoons vegetable shortening, 2 teaspoons vanilla extract, and ⅛ teaspoon table salt. Fit mixer with paddle and mix on low speed, scraping down bowl as needed, until mixture is homogeneous and has texture of Play-Doh, about 2 minutes. Transfer mixture to counter and divide into 12 equal pieces. Roll into balls, place on large plate, and cover with plastic; refrigerate for 30 minutes. Draw or trace 4-inch circle in center of 1 side of zipper-lock bag. Cut open seams along both sides of bag, leaving bottom seam intact so bag opens completely; set aside.
Line 2 rimmed baking sheets with parchment paper. Transfer concha dough to clean counter and divide into 12 equal pieces. Cover loosely with greased plastic. Working with 1 piece of dough at a time (keep remaining pieces covered), form into rough ball by bringing edges of dough together and pinching edges to seal so that top is smooth. Place ball seam side down on clean counter and, using your cupped hand, drag in small circles until dough feels taut and round. Repeat with remaining dough pieces, scraping counter clean with bench scraper as needed. Evenly space 6 dough balls on each prepared sheet. Poke any air bubbles in dough balls with tip of paring knife.
Cover rolls loosely with greased plastic and let rise until doubled in size, 1 to 1½ hours.
While rolls rise, place reserved cut bag marked side down on counter. Place ⅓ cup flour in small bowl; gently toss 1 ball of sugar crust in flour to generously coat, then open bag and place ball in center of circle. Fold other side of bag over ball and, using glass pie plate or baking dish, gently press crust to 4-inch diameter, using circle drawn on bag as guide. Carefully peel bag away from crust to remove, then place crust on top of 1 ball of concha dough, pressing gently to mold crust to dough. Repeat with remaining balls of crust and concha dough, wiping bag clean as needed. (Don’t wait until after dough rises to top dough balls with crust.)
Using butter knife and pressing gently, score crust of each roll with series of concentric curved lines emanating from single point to create seashell pattern, being careful not to cut through topping completely.
Adjust oven racks to upper-middle and lower-middle positions and heat oven to 350 degrees. Bake until buns are golden brown and register at least 205 degrees, 20 to 25 minutes, switching and rotating sheets halfway through baking. Transfer sheets to wire racks and let cool for 15 minutes. Serve.