Bring chicken broth to a boil. Reduce heat; add potatoes, carrots, celery, onion, salt, pepper and thyme. Cover and simmer for 15 minutes, or until vegetables are tender.
Meanwhile, melt butter in a medium saucepan over medium-high heat. Add chopped bacon and cook until crunchy; about 5 minutes. Whisk in flour until smooth. Gradually whisk in milk. Bring to a boil and stir for 2 minutes, or until thickened. Reduce heat and add cotija cheese. Stir cheese mixture and shredded chicken into broth. Cook and stir until heated through.
Sprinkle with chopped parsley, cheddar cheese and ground nutmeg.