Heat olive oil over medium heat in a medium pot. Add carrots and sauté until beginning to soften, about 7 minutes. Season with pepper.
Add broth and ginger to pot, raise heat to high, and bring to a boil. Add fresh peas, if using; cook 2 minutes. Add gyoza to broth and return to a boil. Stir in soy sauce.
Cook gyoza until almost tender to the bite, 2 to 3 minutes (see Notes). Add frozen peas, if using; then cook 1 minute more. Remove ginger slices. Season soup to taste with pepper and stir in parsley. Ladle soup into shallow bowls, top with bean sprouts and green onions, and serve.
Note: Nutritional analysis is per serving.