On medium heat, melt butter, then simmer onion and celery for 5 minutes until soft, but not brown. Add water, potatoes, corn and seasonings. Cover and simmer for 30 minutes or until potatoes are barely tender. Whisk the flour into 1 cup of the Half and Half, and stir into the soup. Add the remaining 3 cups of Half and Half. Simmer for about 15 minutes until the soup has thickened to a creamy consistency.
Correct the seasoning with additional salt and pepper if needed. In order to correct the consistency or the soup you may add a little milk to make it thinner. To make the soup thicker, simmer another 5 to 10 minutes.