Step 1

Make the steamed buns: In the bowl of a stand mixer, combine the water and active dry yeast. Allow the mixture to sit so the yeast can bloom, 10 minutes.

Step 2

Add the remaining steamed bun ingredients to the bowl and, using the dough hook attachment, knead the dough with the motor running just above a stir, 8 to 10 minutes. Shape the dough into a ball and transfer to a greased bowl. Cover the bowl with plastic wrap and let the dough proof in a warm place until it has doubled in size, 1 hour and 15 minutes.

Step 3

While the dough is proofing, make the pickles: Using a mandoline, slice the cucumbers into ⅛-inch-thick slices. In a medium bowl, toss the cucumbers with the sugar and salt, and let sit for at least 10 minutes, then set aside for later.

Step 4

Make the BBQ mushrooms: In a medium bowl, combine the mirin, sake, soy sauce and liquid smoke. Set aside for later.

Step 5

In a small saucepan, add the dried mushrooms and cover completely with water. Cover the mushrooms with a small plate so that they are completely submerged in the water. Bring the water to a boil, reduce the heat and simmer until the mushrooms are completely rehydrated, 5 minutes. Drain the mushrooms and let cool at room temperature. When the mushrooms are cool enough to handle, thinly slice them.

Step 6

In a large sauté pan over high heat, add the olive oil and the sliced mushrooms. Stir the mushrooms a few times to ensure caramelization on both sides and cook for 5 to 7 minutes. Pour the soy sauce mixture over the mushrooms and cook until the liquid has reduced completely, 5 to 7 minutes. Reserve for later.

Step 7

Punch down the dough and transfer to a lightly floured surface. Portion the dough into 24 even handfuls and shape into balls. Cover the portioned dough balls with a lightly dampened towel and let the dough rest again, 30 minutes.

Step 8

Using a rolling pin, roll out the dough balls into 2-inch long ovals. Using your fingertips rub a small amount of vegetable shortening on the ovals, then fold the top over the bottom of each oval, hamburger-style. Shape all the balls into buns, cover once more with a dampened towel and let proof again, 30 minutes.

Step 9

Set up a steamer basket and line with a piece of cut parchment paper. Be sure to leave some of the bottom uncovered so the steam can circulate. Steam the buns for 8 to 10 minutes, then serve with a smear of hoisin sauce, 3 to 4 pickles, a small handful of BBQ shiitake mushrooms and a garnish of green onions.