Golden cheese/broccoli chowder

There were no images on the Internet to do this amazing soup justice. I took this to a relief society dinner last week and it was the only soup gone at the end of the night. It's good stuff!

2 C water
1 C celery, chopped
1 C carrots, chopped
1/2 C onion, chopped
1 pound fresh broccoli, washed and chopped

Cheese Sauce:
1/2 C butter
1/2 C all-purpose flour
2 tsp salt or to taste
1/4 tsp white pepper (I use regular black pepper)
4 C milk (this is good with milk and even better with half-and-half!)
hot pepper sauce, as desired (I have never desired any, so I have never included it at all)
1 pound process cheese spread cut in 1/2 inch cubes or 4 C shredded cheddar cheese (my family makes it with the process stuff and I like it, but have changed to the cheddar and I like that too)
2 C ham, cut in 1/2 inch cubes

In large saucepan, combine water, celery, carrots, and onion. Bring to boil; reduce heat. Simmer, covered for about 5 minutes or until tender/crisp. Add broccoli; cook until broccoli is tender/crisp, about 4-5 minutes. (to keep broccoli bright green, leave the cover slightly ajar.) Do not drain vegetables. To make sauce, melt butter in large saucepan; blend in flour, salt, and pepper. Cook, stirring, for 1 minute. Stir in milk; cook until mixture thickens. Add several drops of hot pepper sauce if desired. Stir in cheese and cook until melted; add the ham cubes. Combine cheese mixture with undrained vegetables; stir to blend. Yield 12 servings.