While the baos are proofing, work on the filling.
Prepare the sour mustard: Wash and rinse the soaked sour mustard with clean water 2 to 3 times. Thinly slice.
Heat a large pan and add the oil. Sauté the ginger, garlic, and chile until fragrant, then add the sour mustard.
Stir-fry for 1 minute, then add the sugar and continue to cook for another minute. Dish out and set aside.
Prepare the braised tofu: Heat a large nonstick pan and add a drizzle of oil. Pan-fry the tofu until golden brown. Transfer to a plate.
Using the same pan, add a little more oil and sauté the ginger until aromatic. Add the garlic, scallion, and chile, and keep cooking until fragrant.
Pour in the water and add the star anise, cinnamon stick, and season with the sauces, sugar, sesame oil, white pepper, and salt (if needed).
Add the tofu back to the pan and bring the mixture to a boil.
Now drop the heat to medium and simmer until the sauce is reduced to one-third of its volume.
Remove the ginger, garlic, scallion, chile, star anise, and cinnamon. Combine the cornstarch with ½ teaspoon water, then stir this slurry into the sauce to thicken the sauce. Turn off the heat.
Cook the proofed bao: Turn on the heat to high and bring the water to a boil. Lower the heat to medium-high and steam the bao for 8 minutes. Turn off the heat and let them stay in the steamer for another 8 minutes before removing them.