Melt the butter in a large heavy pot over low heat. Add the onions, cover, and cook, stirring occasionally, until the onions are tender and lightly colored, about 25 minutes.
Add the stock and bring to a boil.
Scrub the zucchini well with a kitchen brush, trim the ends, and chop coarsely. Drop the zucchini into the stock and return it to a boil. Reduc