Heat the olive oil in a large pot over medium heat. Add the pork tenderloin pieces and cook until lightly browned on all sides, about 5 minutes.
Stir in the diced onion, minced ginger, and minced garlic. Cook for 2 minutes until the onion softens.
Add the sliced shiitake mushrooms and carrots. Cook for another 3 minutes, stirring occasionally.
Pour in the chicken broth. Bring the mixture to a simmer and cook for 15 minutes until the carrots are tender.
Add the snap peas and cook for 3 more minutes until they turn bright green but stay crisp.
Season with salt and pepper to taste. Ladle the stew into bowls and top with sliced green onions.