Melt butter in large deep pot with a lid and add leeks, onions, carrots, and garlic. Stir well, then sprinkle sugar over all and cover tightly. Cook over lowest possible heat for 20 minutes; do not allow to burn.
Place butternut squash into a microwave safe dish, add a little water, and cover with plastic wrap. Place in microwave and cook on high for 15-20 minutes until very soft.
When vegetables in the pot are cooked, add zucchini and 2 cups of the chicken stock, plus the white pepper and salt. Cook, uncovered, over medium heat until zucchini are very soft, about 10 minutes.
Transfer vegetables and liquid to a food processor. Scoop out the pulp of the squash, and add to food processor. Puree everything together, adding some of the remaining stock if necessary (you may have to do the processing in two or three batches), then return the pureed soup to the pot and stir to mix evenly.
Stir in remainder of stock until you reach the consistency you prefer and reheat. Correct seasonings if necessary.
I found that if I use canned chicken broth it will be a blander soup than if I use a homemade chicken stock so you may have to adjust seasonings accordingly depending upon which you use.
For the leeks, use only the white part, washed.
Adapted from recipe from Soup Meals by Lee Bailey, as reprinted in New Woman magazine, July 1989.