Ingredients

Potatoes (5 to 6)
Salt (half teaspoon to start)
Pepper (4th teaspoon or less if you don't like a stronger pepper flavor)

Chicken bouillon (measurements based on brands)
If you use Better Than Bouillon brand (use 1 tablespoon)
If you use Knorr brand then (use half a cube)
I've only used Better Than Bouillon

Half and half (1 cup)
don't use low fat milk cause it will curdle

Corn starch (2 tablespoons)
Butter (3 tablespoons)
Celery which is optional (add as much as you want but I use half a cup)
You could add onions also, I haven't tried it but it seems like it would go well

Water

To start
Peel and wash potatoes
cut potatoes in half and then into cubes (about an inch thick)
Add potatoes to pot and then put in enough water that potatoes are just covered over the tops with the water
Add chicken bouillon (I've used beef too, they both turn out good)
Add celery after washing and cutting it into small pieces, size to your preference (if you want it) 
Bring to boil
Let it continue to boil for 10 to 13 minutes or until potatoes are easy to poke through with a fork

In another bowl
Pour in 1 cup of half and half
Add 4th teaspoon pepper
Add half teaspoon salt
Add 2 tablespoons cornstarch
Stir thoroughly

Pour half and half mix into boiling pot of potatoes
Stir well
Add 3 tablespoons of butter and stir until butter is melted

Let continue to cook for 5 minutes stirring occasionally
Add salt to taste
You can also add cheese, I'd say cheddar, grated up and stirred in until it's melted and mixed well

Reduce heat and let it cook longer (5 to 10 minutes more) for thicker soup, just keep in mind that soup will thicken when it cools

It's ready at that point if you want but I wait until it's cooled, then store it in the fridge for about 10 hours (next day) before having it though.