How to Make It
Whisk together soy sauce, vinegar, brown sugar, and garlic in a medium bowl. Add shiitakes, and toss to coat. Let marinate at room temperature 15 minutes. Drain and discard marinade.
Cut pizza dough into 12 (11/4-ounce) pieces. Using oiled hands, gently shape into balls (do not press out the air). Sprinkle dough balls with sesame seeds, and transfer to a plate.
Fill a medium pot with water to a depth of 1 inch; bring to a simmer over medium. Line 2 baskets of a 2-tier, 91/2-inch round bamboo steamer with parchment paper. Spread shiitakes in 1 basket; fit inside pot. Arrange dough balls in second basket; fit on top of first basket. Cover and steam until shiitakes are tender and buns are puffed, 15 to 20 minutes.
Remove shiitakes and buns from steamer baskets. Carefully split each bun, leaving one end attached. Fill buns evenly with shiitakes; top with cucumber, carrot, and scallion. Serve, passing hoisin sauce at the table.