Activate the yeast: Whisk the water, sugar and yeast together in the bowl of your stand mixer. Cover and let the yeast bloom until frothy and fragrant, about 15 minutes.
113 grams water, 50 grams sugar, 10 grams active-dry yeast
Make the dough: Add the sourdough discard, egg and egg yolks to the yeast mixture. Mix with the dough hook until no traces of yolk or starter remain.
1 large egg, 80 grams egg yolks, 113 grams sourdough discard
Add the dry ingredients in and mix until a shaggy dough forms.
480 grams all-purpose flour, ⅛ teaspoon ground green cardamom, 9 grams salt
With the mixer running on low speed, add the butter 1 tablespoon at a time, waiting until each addition is fully incorporated before adding more. The dough may look greasy at first but will become smooth and cohesive as the butter is absorbed.
113 grams unsalted butter
Continue kneading the dough with the dough hook until it pulls away from the sides of the bowl and clings to the hook, about 3 to 5 minutes. Add the chocolate chips and mix until evenly distributed, adding them at this point prevents them from getting crushed and coloring the dough.
180 grams dark chocolate chips
Cover the bowl with plastic wrap and let the dough rest for 15 minutes. Turn the dough out onto a clean surface and lightly knead until smooth and elastic. Round the dough into a tight ball
Let the dough rise: Transfer the dough to a lightly-oiled bowl, cover with plastic wrap and let rise until doubled in volume, about 1 to 2 hours.
Shape the dough: Line 2 large baking sheets (18 by 13 inches) with parchment paper. Turn the dough out on a lightly floured surface. Flatten the dough lightly into a disc. Using a bench scraper, divide the disc into 8 even portions. Cover the dough with plastic wrap to prevent them from drying out.
Take one wedge of dough and flatten it into a rough rectangle. Fold the corners towards the center and pinch the seam shut. Turn the dough over and lightly drag it in a circular motion on your work surface. Transfer the dough to your prepared baking sheet.
Repeat with the remaining portions of dough and arrange the dough with space to rise on the baking sheets.
Give the dough a final rise: Let the dough rise untouched until puffy and doubled in volume, about 45 minutes to 1 hour.
Prep: When the dough is close to being ready, preheat your oven to 325 F. Combine the egg yolk and water and break the mixture up with a fork.
1 egg yolk, 6 grams water
Brush the surface of the dough with egg wash. Using a lame fitted with a sharp blade, score a shallow ring around the circumference of each bun.
Bake: Bake for 25 to 30 minutes or until golden brown and the buns register at least 200 F when probed with an instant-read thermometer.