Combine water, potatoes, carrots, celery, onion, salt and pepper in a large kettle. Boil 10-12 minutes. Meanwhile, in a small saucepan, make white sauce by melting the butter. Add flour and stir until smooth, about 1 minute. Slowly add milk; cook until thickened. Add grated cheese to white sauce; stir until melted. Add white sauce and cubed ham to vegetables that have not been drained. Heat through.
Microwave Option: To make white sauce in microwave, melt butter, then add flour and stir until smooth. Add milk and stir. Microwave on med and stir often until thickened. Finish as above. Cheese should melt without additional heating.
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