To begin, dissolve the yeast and 1 tbsp of sugar in the warm water. Let it sit for 5-10 minutes until the mixture becomes frothy. In a large bowl, combine flour, remaining sugar, salt, and baking powder. Add the yeast mixture, warm milk, and vegetable oil, mixing until a dough forms.
Knead the dough on a lightly floured surface for 8-10 minutes, until it becomes smooth and elastic. Place the dough back into the bowl, cover with a damp cloth, and let it rise in a warm area for 1-1.5 hours or until it doubles in size.
While the dough rises, prepare the filling. In a mixing bowl, combine the ground pork, chopped onion, fish sauce, soy sauce, sugar, black pepper, and diced mushrooms. Mix until all ingredients are well incorporated, ensuring a flavourful, balanced filling.
Divide the filling mixture into four equal portions, shaping each into a small ball. Gently flatten each portion and place a boiled quail egg in the centre, folding the pork mixture around the egg to encase it fully. Set aside for assembly.
Once the dough has doubled in size, punch it down and knead briefly to release any air bubbles. Divide the dough into four equal portions, rolling each into a smooth ball. Flatten each ball into a disk, about 5 inches in diameter, for filling.
Place one portion of filling in the centre of each flattened dough disk. Gently gather the edges of the dough, bringing them up over the filling and pinching them together at the top to seal. Twist lightly to secure, forming a closed bun shape.
Prepare a steamer and bring the water to a gentle simmer. Place each bun on a square of parchment paper and arrange them in the steamer, leaving space for expansion. Steam over medium heat for 15-18 minutes, keeping the lid slightly ajar during the first 5 minutes to prevent condensation from dripping onto the buns.
Serve the steamed buns warm, either as they are or with a side of soy sauce for dipping. Bánh Bao is perfect as a snack or light meal, showcasing a tender, slightly sweet dough with a savoury filling. Enjoy the flavors and texture, and savour the taste of traditional Vietnamese cuisine!