Bring 2 quarts water to a boil in a large saucepan. Add tortellini; cook 4 minutes. Add broccoli, and cook an additional 5 minutes or until tortellini is tender. Drain in a colander; set aside.
Heat the oil in pan over medium-high heat. Add mushrooms, chopped onion, and shrimp; saute 3 minutes or until shrimp is done. Add ginger, salt, and broth; bring to a boil. Add tortellini mixture, and cook until thoroughly heated. Ladle soup into individual bowls, and garnish with onion rings, if desired.
Note: Because this recipe uses only half the package of tortellini, freeze the remaining half in an airtight container.