Preheat the oven to 375 degrees . Line a baking sheet with parchment paper. Brush the cut sides of the squash and the garlic cloves with the olive oil; season with salt and pepper. Place the squash cut sides down on the baking sheet, tucking the garlic cloves and thyme into the squash cavities. Roast until tender, about 45 minutes.
Meanwhile, place the potato in a medium saucepan and fill with enough water to cover by 1 inch. Bring to a low boil and cook until tender, about 15 minutes. Drain and set aside.
When the squash is cool enough to handle, remove and discard the peel and the thyme. cut the squash into large pieces. In a blender, working in batches, puree the squash, garlic cloves, potato and chicken broth. Season with salt and pepper.
In a medium saucepan, heat the soup over medium-low heat until warmed through. Divide among 4 serving bowls and top with the yogurt, onions and parsley.