Combine water, vegetables, salt, and pepper and boil 10-12 minutes until vegetables are tender.
In a small saucepan, make white sauce by melting the butter, then add flour and stir until smooth, about 1 minute. Slowly add milk; cook until thickened. Add cheese to white sauce; stir until melted.
Add white sauce and cubed ham to vegetables that have not been drained. Heat through.