Melt the butter in a 5-quart pot over low heat. The butter shouldn't color at all.
Add the diced leeks; stir in the salt and pepper.
Cover the pot, and let the leeks sweat until perfectly tender -- about 10 minutes.
Add the water, and bring to a boil over high heat.
Add the cornstarch mixture, and stir until the the water thickens -- about 30 seconds.
Add the potatoes, partially cover the pot, and let simmer until tender — 20-30 minutes.
Puree the soup with an immersion blender.
Then stir in the parsley and the cream.
Serve hot, warm, or cold, garnished with extra parsley and, if desired, small croutons.
