In a large saucepan, combine the potatoes, water, carrot and onion. Bring to a boil.
Reduce heat cover and cook until tender, 10-15 minutes.
In another saucepan, melt butter. Stir in flour until smooth.
Gradually stir in milk; add salt and pepper.
Bring to a boil; cook and stir until thickened, about 2 minutes.
Stir in cheese until melted.
Stir into broth and vegetable mixture.
Add ham and peas; heat through.