Melt butter in a kettle
Saute garlic clove, celery, onion, and carrots in butter - about 3-5 minutes
Add chicken broth and potatoes, then add thyme, salt and pepper
Cook until potatoes are tender then add corn (optional)
Add flour and stir until smooth
Add milk and mix together well
Heat on medium heat, stirring until the sauce thickens (this can take several minutes)
Add chicken and then add cheese, stirring until the cheese is melted
Serve and enjoy!
OPTIONAL: You can saute and cook all the vegetables and make your white sauce in a separate kettle, then combine the two before adding the cheese. You'll have two kettles to wash instead of one, but you can be working on both at the same time.