Preheat the oven to 425 degrees. Line a baking sheet with parchment paper.
Season the squash with salt and pepper and tuck 2 sprigs of thyme into each cavity. Place, cut side down, on the baking sheet and roast until fork-tender, about 40 minutes.
When the squash is cool enough to handle, discard the thyme; peel the squash and coarsely chop. Combine the squash, garlic, and 1/2 cup of the chicken stock in a food processor and puree until smooth.
Add the remaining stock gradually until the mixture forms a very loose puree. Season the soup with salt and pepper.