Place squashes on a paper towel and microwave on high just until tender when pierced with the tip of a paring knife, 8 to 10 minutes. Remove from the microwave, and halve each squash lengthwise (to speed cooling). When cool enough to handle, scoop out and discard the seeds. Scrape out flesh into a bowl; discard skin. (To prepare in oven, preheat oven to 450 degrees. Halve squash lengthwise; scoop out and discard seeds. Place squash, cut side down, on a rimmed baking sheet; cover tightly with aluminum foil. Roast until almost tender when pierced wtih a knife, 15 to 25 minutes. When cool enough to handle, scrape out flesh, discard skin, and proceed with step 2).
In a large saucepan, heat butter over medium. Add onion; season with salt and pepper. Cook, stirring occasionally, until tender, 3 to 5 minutes. Add squash, thyme, broth, and 2 cups water. Bring to a boil over high heat; reduce to medium, and cook until squash is very tender, 10 to 12 minutes.
Working in batches, puree mixture in a blender until very smooth, about 1 minute. Return to pan; add half-and-half, and season generously with salt and pepper. Thin bisque, if needed, by adding more water. Serve garnished with thyme.