Heat olive oil in a large heavy pot over low heat. Add garlic, onions and ginger; sauté until soft and golden, about 10 minutes, stirring frequently. Add carrots and parsnips; cook, covered, until vegetables are tender, about 10 minutes.
Add broth, salt and pepper. Bring to a boil over high heat; reduce heat and simmer 20 minutes.
Add shredded chicken and noodles; simmer until thoroughly heated.