Preheat oven to 350°.
Cut squash in half lengthwise; discard seeds and membrane. Brush cut sides of squash halves, cut sides of onion quarters, and garlic cloves with oil. Arrange squash halves, cut sides down, on a jelly-roll pan; arrange onion quarters and garlic cloves on pan. Bake at 350° for 45 minutes or until tender. Cool slightly. Peel squash. Squeeze garlic cloves to extract pulp.
Place squash, onion, and garlic pulp in a food processor; process until smooth. Add crème fraîche and remaining ingredients; process to combine. Serve warm.
Refrigerate in a microwave-safe container, then reheat in a microwave on HIGH for one to two minutes or just until warmed.