Toss chicken with cornstarch and soy sauce, set aside.
Heat oil in a large saucepan over medium heat. Add onion, mushrooms, carrots and red pepper; cook until vegetables are tender-crisp, about 3 min. Add ginger and garlic and cook until fragrant, about 1 min. Add chicken and cook 2 min. Add chicken broth; increase heat to medium-high and bring to a boil.
Reduce heat and simmer until chicken is fully cooked and vegetables are tender, about 15 min. Ladle soup into bowls; top with green onions.
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