Heat the vegetable oil in a large pot over medium heat. Add the pork chop pieces and cook until lightly browned on all sides, about 5 minutes.
Add the onion, garlic, and ginger to the pot. Stir and cook for 2 minutes until the onion starts to soften.
Add the shiitake mushrooms and cook for another 3 minutes, stirring occasionally.
Pour in the chicken broth and soy sauce. Bring the mixture to a simmer, then reduce the heat to low, cover, and cook for 15 minutes.
Stir in the bok choy and simmer uncovered for 5 more minutes until the bok choy is tender but still bright green.
Remove from heat and sprinkle with sliced green onions before serving.