Melt butter in a large, heavy pot. Add celery and onions. Saute until wilted and onion is opaque. Add 2 quarts of water and bouillon cubes. Simmer until bouillon dissolves. Add potatoes. Add more water if needed to just cover vegetables.
Simmer until potatoes are tender. Scoop out 1 1/2 cups of potatoes and mash into paste. Return them to pot and stir. Add enough milk to give soup a white milky look. Lower heat and simmer very slowly stirring often. Soup will thicken slightly.
Store leftovers well covered. If soup becomes too thick when reheated add a little milk.
