Set the pressure cooker to sauté and add the oil. When the oil is hot and just barely smoking, add the pork. Cook, stirring frequently, until the pork is browned - about 4-6 minutes.
Add the onion and cook for about 3 minutes or until the onion is softened. Add the mushrooms and cook for about 3 more minutes.
Add the chicken stock, kale, water, ginger, garlic, red pepper flakes and black pepper.
Cancel the sauté feature and lock the lid in place. Be sure the vent is set to sealing. Set the pressure to high and the time for 10 minutes.
While the soup is cooking, cook the noodles according to package directions.
When the time is up, let the pressure release naturally for 10 minutes then do a quick pressure release by turning the knob to venting. When the pressure valve drops, remove the lid, stir and taste to adjust seasonings.
Divide the noodles between the bowls and ladle the soup on top. Serve with radishes and green onions if desired.