Dice the potatoes into the size you desire, and add it to the 3-4 cups water when boiling. Dice some of the pieces smaller than the others so they boil away. Add to the thickness and taste of the soup. Add the chopped celery.
Add the oil to a skillet and fry the diced onion until soft. Add to the potatoes and celery. Boil until the potatoes are sufficiently cooked, and turn the flame to low.
Add three cans of the cream of celery and stir until evenly mixed. Add the fourth can if you so desire for taste (I always do.) Add the Liquid Smoke and parsley. Add salt and pepper to taste.