Place the diced potatoes in a pot with the 4 cups of chicken broth and bring to a boil. Reduce heat and simmer for about 15 minutes or until potatoes are nice and tender.
While potatoes cook, in a separate pot, melt the butter. Add the chopped green onion and sauté for 5 minutes.
Whisk the flour, celery seeds and paprika into the butter/green onions and stir constantly until a smooth paste. Gradually stir in the ff half and half. Stir frequently until mixture begins to thicken.
Add the hot cooked potatoes and both into the creamy mixture; stir well.
With a slotted spoon remove 1 or 2 cups of the potatoes and set them aside.
Use a stick blender or blender or food processor to blend the soup in the pot.
Return the blended mixture and reserved 1 or 2 cups of potatoes to the pot.
Stir in the cheese, salt and pepper.
Stir and cook (but do NOT allow to boil) until cheese is melted smooth and well-mixed.