In large pot, boil potatoes in water 10 minutes. Drain and set aside. In large heavy pot, sauté bacon, onion and celery over medium-high heat until celery is tender, about 5 minutes.
Remove mixture from pot, drain bacon grease and return mixture to pot. Add milk, water, base, salt and pepper. Cook over medium-high heat until mixture is very hot, about 8 minutes, stirring often. Do not let mixture boil.
In small, heavy saucepan melt margarine. Add flour and mix well. Cook over medium-low heat until mixture bubbles, stirring 2 to 3 minutes to make a roux. While constantly stirring soup, add roux slowly until soup is thick and creamy, about 4 minutes.
Stir in parsley, reserved potatoes, and cream. Garnish with cheese, bacon bits, onions or all three.