Potato Soup for St. Pat's Day

I haven't made Potato Soup in years, but for St. Patrick's Day I thought that I would give it a try. It turned out amazingly good. When I was a kid my mom used to make potato soup and we would have it with lots of saltine crackers in it (crushed of course). Her soup was basic potato, milk, celery, onions, and a little butter. She never thickened it or mashed the potatoes and she used a lot of celery. I loved it! My taste is a little different now that I'm no longer seven so here is how I made my new version. I think the carrots make the soup extra good.

St. Pat's Day Potato Soup

2 T butter (use more if you like)
1/2 yellow onion, finely chopped
1 rib celery, finely chopped
1 small carrot, finely chopped
Sauté in large sauce pan until tender but not browned. Add in:
1 14.5 oz. can low sodium chicken broth
2 cups water
1 chicken bullion cube
4 medium russet potatoes, peeled and cubed in bite size cubes
Bring to a boil and simmer until the potatoes are tender. Use the back of a spoon to mash some of the potatoes, but not all.
Add:
1/2 cup Half and Half
3 T mashed potato flakes or granules
3 T Neufchatel Cheese or Cream Cheese
Stir until the cheese melts and the soup thickens
(Optional) Stir in: 
1 medium russet potato, baked and cut into small cubes, with or without skin
Serve while HOT! Don't burn your tongue :)
You can leave out the cheese and mashed potato flakes if you like a thin soup.

HAPPY ST. PATRICK'S DAY!