In a large saucepan, heat canola oil over medium heat. Add mushrooms and carrot; cook and stir until mushrooms are tender, 6-8 minutes. Stir in garlic and ginger; cook 1 minute longer.
Stir in broth, soy sauce and sesame oil. Bring to a boil. Add shrimp and ramen (discard seasoning packets or save for another use). Simmer until shrimp turn pink and noodles are tender, 4-6 minutes. Garnish with green onions and, if desired, cilantro.