In a large saucepan, heat the oil over medium heat. Add in the onion, garlic, celery and bell pepper until the vegetables begin to soften.
Mix in the chicken broth and bring to a boil. Reduce heat and simmer for around 10 minutes.
Mix in the frozen mixed vegetables and corn and simmer for around 5 minutes.
In a medium bowl, whisk together the flour and milk until smooth.
Slowly mix the milk mixture into the soup. Add in the salt, pepper and cayenne pepper, stiring until thickened, around 15 minutes.
Mix in the chicken and cheese until the cheese is melted. Enjoy warm.