Add the carrots, celery, garlic, onion, chicken, buffalo sauce, and chicken stock to the crock pot. Cook on low for 3 1/2 hours.
Add the egg noodles, raise the temperature to high, and cook for a half hour.
Remove the chicken breasts to from the crock pot, shred the chicken and return it to the crock pot.
Turn off the crock pot and stir in the heavy cream. Serve topped with blue cheese crumbles.