Preheat oven to 400 degrees. cut 1/3 inch off the top of the garlic head, exposng the cloves. Arrange the garlic, squash, and onion cut side up in a large baking dish. Drizzle the vegetables with olive oil. Scatter the thyme over the vegetables.
Cover the dish tightly with foil and bake until squash is tender when pierced with a knife, about 1 hour.
Scrape squash from he skin into the processor work bowl. Peel outer layers and trim root end from onion halves. Add onion to processor. Separate 6 garlic cloves from head and squeeze the garlic to the bowl. Puree vegetables until smooth. Add more roastd garlic if desired.
Transfer puree to heavy large pot. Wisk in 2 cups of chicken broth. Stir over medium heat until heated through, adding more broth if desired.
Season with salt and pepper.
Ladle into bowls and garnish with parsley.
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