Soak the Dried Shiitake Mushrooms and Dried Wood Ear Mushrooms in warm water for 20–30 minutes until soft; squeeze out excess water and finely chop. Soak the Glass Noodles in the same warm water until pliable, then drain and roughly chop.
Bring a small pot of Water to a gentle boil, add a splash of White Vinegar, then lower in the Quail Eggs and cook for 3–4 minutes for a soft-cooked center or 5–6 minutes for fully set yolks. Plunge into cold water and peel.
Heat a skillet over medium heat and brown the sliced Chinese Sausage to render its fat; remove and set aside. In the rendered fat (or a little Neutral Oil if needed) sauté the diced Onion and minced Garlic until soft and fragrant.
Add the Ground Pork to the pan and cook, breaking it up, until no longer pink. Stir in the chopped mushrooms, chopped glass noodles, sliced back in Chinese Sausage, and chopped Scallions.
Season the filling with Fish Sauce, Oyster Sauce, a pinch of Sugar, and Ground Black Pepper. Mix a small slurry of Cornstarch with a little cold Water and stir into the filling to thicken; cook briefly until the mixture is cohesive but not wet. Taste and adjust seasoning, then let the filling cool.
Make the dough by combining All-Purpose Flour with Instant Yeast, Baking Powder, a pinch of Salt, and a little Sugar if you like it slightly sweet. Add warm Milk and Neutral Oil and mix until a soft dough forms.
Knead the dough on a lightly floured surface until smooth and elastic, about 8–10 minutes. Place in a lightly oiled bowl, cover, and let rise until doubled in size, about 60–90 minutes depending on room temperature.
Punch down the dough and divide it into even pieces (about golf-ball to tennis-ball size, depending on how large you want the buns). Flatten each piece into a disc, place a spoonful of the cooled filling in the center and, if using, top with a peeled Quail Egg. Gather and pinch the dough to seal, forming a smooth bun and place seam-side down on a small square of parchment.
Arrange the buns with space between them, cover, and let them rest for 20–30 minutes for a short second rise.
Steam the buns over boiling water for 12–15 minutes (adjust time for size). After turning off the heat, leave them covered for 3–5 minutes before removing the lid to prevent collapse.
Serve the Bánh Bao warm. They are best eaten fresh but can be reheated gently by steaming for a few minutes.
