Boil enough water in a pot to boil all of your beef.
Once the water is boiling, add the beef. Let it come back up to a boil, and boil for 1 minute.
Strain in a colander and rinse thoroughly with fresh water to remove any impurities.
In your instant pot, turn on the saute setting. Add the oil, crushed ginger, garlic, scallions, and onions in that order. Stir to lightly caramelize. Let the onion turn translucent.
Add the tomato and dried chilies. Mix well.
Add the meat, tomato paste, spicy bean paste, sugar, soy sauce, and Shaoxing wine, and mix thoroughly.
Pour 8 cups of water into the instant pot. Add the spice packet. The instant pot should be filled to the 10-cup line; it shouldn’t be more than ⅔ of the way full per safety instructions.
Close the lid of the instant pot, and make sure you have your vent set so it is not venting. Cook for 100 minutes on the aromatic meat stew setting.
When the instant pot timer is up, carefully release the pressure valve (wear an oven mitt, so you don’t scald yourself!).
Boil some noodles per package instructions, and in the last minute or two of the noodles cooking, throw your bok choy in and blanch until just tender.
Serve each bowl of Taiwanese beef noodle soup with a serving of noodles, a few stalks of bok choy, and generous sprinklings of finely minced cilantro, scallions, and Chinese pickled mustard greens.
DONE!