Combine turkey and onions in a large stockpot over medium-high heat; cook until turkey is no longer pink and onions are translucent, about 6 minutes. Drain and discard fat. Add garlic; cook, stirring occasionally, until fragrant, about 2 minutes.
Pour chicken broth into the stockpot with the turkey and bring to a boil. Add potatoes, carrots, corn, celery, peas, green beans, tomato paste, Worcestershire sauce, soy sauce, basil, bay leaves, salt, and pepper. Return to a boil, cover, and reduce heat to low. Simmer until vegetables are soft, about 30 minutes.
