Chop onion, carrots, celery, and garlic

In large pot melt butter. Add chopped veggies and saute on low heat until soft

Add flour, salt, and pepper to pot and stir until smooth

Add broth, milk, and potatoes. Set on high heat until boiling then cover and cook on low to medium heat for about 10-15 mins.

Add broccoli and parmesan cook uncovered for about 5mins.

Add cheddar and American cheese, stir well and remove from heat

Remove some potatoes and broccoli, blend it up and add it back to soup to thicken it some