In a skillet, melt the butter. Saute onion, carrots, and celery in the butter until onions are just soft. Add to the crock pot along with the chicken broth, cream of soup, and milk. Stir until combined.
Add in the chicken and corn or peas. Stir then cook on high for 3 1/2 to 4 hours on high or 6 hours on low.
Stir in the noodles and turn to high if not already cooking on high. Allow to cook for 45-60 minutes until the past is tender. Serves 6.