Rachel's Cheesy vegetable and ham chowder

I put out a plea on facebook for leftover easter ham recipes. The smallest ham I could find this year was 9 lbs. That's a lot for 2 adults and my 2 year old. (my 5 year old won't touch ham.) This recipe was given to me by my neighbor, Rachel. It was delish! Thanks Rachel.
 
Rachel's cheesy vegetable and ham chowder
3 1/2 cup chicken broth
8 celery ribs sliced
4 carrots sliced
2 peeled, cubed potatoes
1 large chopped onion
1/2 tsp pepper
1/4 c butter
1/4 c flour
2 c milk
2 c shredded cheese
1 bag frozen corn (I did not add this.. I have a thing against corn in recipes.. )
2 c cooked cubed ham
 Bring broth to boil. Add celery, carrots, potatoes, onion and pepper. Cook until veggies are tender. In a glass cup melt butter and add flour to it. Whisk until smooth. Add to vegetables. Add milk and cheese. Add corn and ham. Heat and serve. Makes 10 cups.