Make the tangzhong by whisking together bread flour and milk in a microwave-safe bowl, then microwaving in 30-second increments and whisking to remove lumps until it reaches a pudding-like consistency.
Make the dough by adding the tangzhong to a stand mixer bowl with butter, egg, sugar, milk powder, and salt. Let it cool, then add bread flour and instant yeast and knead for 5-8 minutes until smooth and elastic.
Prepare the Chinese BBQ marinade by mixing together honey, hoisin, spices, garlic, and soy sauces.
Tenderize the pork or chicken by pounding, mixing with baking soda and water, then marinating in the BBQ sauce.
Cook the marinated meat in a skillet until charred and glazed.
Make the mushroom filling by rehydrating dried shiitake mushrooms, sautéing fresh mushrooms, and combining with the BBQ marinade.
Prepare the filling base by making a starch slurry and mixing it with soy sauce, honey, and spices.
Assemble the buns by shaping the dough into balls, flattening, adding filling, and pleating the dough to seal.
Proof the shaped buns until puffed up, then brush with egg wash and bake at 350°F for 18-20 minutes until golden brown.
