Combine warm water, sugar, and yeast in a measuring cup or bowl. Stir with a spoon to mix and allow yeast granules to dissolve, about 5 to 10 minutes.

Place bao flour/all-purpose flour in a large bowl. Add powdered/icing sugar and stir to combine. Make a well in the center of the bao flour.

Pour proofed yeast mixture into the well of the bao flour. Stir and mix with a spatula. Also, give it a quick knead to bring the dough together.

Add vegetable oil and continue mixing to form a dough ball. Cover bowl with plastic wrap and allow it to rest for 5 minutes.

After 5 minutes, continue to knead the dough until it is smooth, about 3 minutes.

Cover the bowl with plastic wrap and allow dough to rise in a warm place for about 1¼ hours or until double in size.

Combine bite sized chicken thighs, minced garlic, grated ginger, salt, ground pepper, dark soy sauce, and sesame oil in a medium sized bowl. Mix well and divide into 4 portions. Set aside.

Place ground pork in a medium sized bowl. Remove preserved mustard stems from package and give it a rough chop. Transfer to bowl with the ground pork. Add salt, ground pepper, and sesame oil. Mix well and divide into 4 portions. Set aside.

When dough has more or less doubled in size, remove the plastic and gently gather and flip the dough.

Sprinkle baking powder all over the dough. Knead until all baking powder is incorporated.

Remove dough from bowl and continue to knead on a lightly floured surface for 4 to 5 minutes.

Shape dough into a longish shape and cut into 4 equal pieces. Shape each piece of dough into a ball. Place the pieces of dough into the bowl and cover the bowl with plastic to prevent them from drying.

Take a ball of dough from the bowl and flatten it into a disk. Using a small rolling pin, roll out the edges to form a wrapper of about 8 inches in diameter with a slightly thicker center and tapered edges. Place the dough wrapper on the small shallow bowl.

Arrange a portion of chicken filling, pork filling, half an egg, and 4 quarter pieces of Chinese mushroom in the middle of wrapper. Gather and pleat the edges with your thumb and index finger. Then, twist and pinch to seal. Carefully transfer the formed bao onto a piece of prepared parchment paper and into a steaming rack. Repeat with remaining dough. Do not crowd the rack with too many baos as they will expand during steaming.

Place steaming rack over a pot of cold water on the stove. Cover with lid and turn on the stove over medium high heat.