To make the dough: In a medium bowl or the bowl of a stand mixer, combine all the dough ingredients and knead — by hand or with a mixer — to make a soft, elastic dough, about 8 to 10 minutes in a stand mixer. (It’ll take a bit longer to knead by hand.)
Place the dough in a lightly greased bowl, cover, and let rise for 1 to 1 1/2 hours, until it's nearly doubled in bulk.
To shape the buns: Gently deflate the dough and divide it into 12 pieces (about 58g each). Cut out twenty 4" squares of parchment and set aside.
Take 2 pieces of the dough and divide them each into 5 pieces so that you end up with 10 pieces (about 11g each). Roll them into small, stubby logs, about 1 1/2" to 2" long, with one end tapered and slightly pointy; these will be the stems of the mushroom buns. Don’t worry if they’re not all exactly the same. Place each of the stems on its own parchment square, cover, and let rest while you shape the rest of the dough.
Take the remaining 10 pieces of the dough and shape into 10 smooth round balls. Working with one piece of dough at a time, use your floured palms to flatten the balls into rounds about 2 1/2" to 3" in diameter. Place a scant tablespoon (8g) of chocolate chips in the center of the round and gently pull the sides of the dough in towards the center to cover the chocolate and re-form a ball. Pinch the dough together to seal and let rest seam-side down. Lightly cover as you fill the remaining dough balls with chocolate.
To make the glaze: In a small bowl, combine the cocoa and water. Add more water, a teaspoon at a time, until you have a thick, paint-like paste. Mix thoroughly.
With a pastry brush, brush the chocolate glaze on the tops of the chocolate-filled buns. Place each of the buns on a parchment square and tent with plastic wrap or a reusable cover to avoid touching the tops of the buns. (You can place the buns in a baking dish, then cover the dish, or you can use jars or cans to prop up the plastic wrap.)
Let the buns rise in a warm spot until they’re puffy and the chocolate glaze has started to crack and form a mosaic pattern, about 40 to 60 minutes.
To steam the buns: While the dough is rising, set up your steamer. You can use a tiered bamboo steaming tray or a stock pot with steaming inserts. If using a bamboo tray, bring a shallow pan of water to a boil; if using steaming inserts, bring a pot of water to a boil. Lower heat to medium to maintain a steady simmer.
First, steam the stems. Place the stems in a single layer and steam for 13 minutes, then remove from heat. Leave the lid on for another 5 minutes before uncovering (this will help prevent them from collapsing).
Repeat the steaming process with the chocolate-filled buns, being sure to leave a few inches between each, as they will expand during steaming. These buns also benefit from a 5 minute rest after steaming with the lid on to ensure the structure is set.
To assemble: When buns are just cool enough to handle, use scissors to cut a small 1/4" hole in the bottom of each of the chocolate-filled buns and gently insert one of the stems about 1/2" into the cap, twisting gently to adhere. Repeat with the remaining buns and serve immediately.
Storage information: Any leftover chocolate mushrooms should be cooled completely and then stored, well wrapped, before being frozen. To reheat frozen buns, wrap with microwave-safe plastic or a wet paper towel and heat in the microwave for about 45 seconds.
