Cheesy Chicken Vegetable Soup

I never would have tried this soup had I known it contains Velveeta. Let's just say my prejudices against Velveeta are extinct. This is a delicious soup. (You may remember it from the first annual Westerberg Christmas party.)
From my friend Emily Morrison, who is an excellent cook.

4 c. water
1 c shredded or chopped carrots
1 c. diced celery
2 c. cubed potatoes
1 medium onion
4 chicken bouillon cubes
Combine above ingredients and cook 15 min. Add the following a cook 15 more.
1 (10 oz) frozen broccoli
1 (10 oz) frozen cauliflower
Add the following:
2 cans cream of chicken
1 lb Velveeta, cubed
1-2 cups cubed cooked chicken breast pieces.
Heat through and serve.