Mom's Ham & Potato Soup

This is my all time favorite soup from my Mom.

Boil 4 C water in a large pot then add:
4 C chopped potatoes
1 C chopped carrots
1 C chopped celery
1/2 c chopped onion
Steam 15 min.
Add:
1 tsp Salt
1/2 t Pepper
2 C diced Ham
Simmer.
In another pan mix (sauce)
1/2 C butter
1/2 C flour
4 C milk
Whisk and cook on medium heat until thick.
Add sauce to vegetables. cook 2 more minutes. Add
3 C shredded cheese