Preheat your oven to 400°F (200°C) and line two baking sheets with parchment paper.
Peel and cube the butternut squash into 1-inch pieces, then place them on the first baking sheet with the chopped onion and the whole garlic clove.
Drizzle the vegetables with half of the olive oil and season with half of the sea salt and black pepper; toss to coat evenly.
Place the chicken breast on the second baking sheet, drizzle with the remaining olive oil, and season with the remaining salt, pepper, and dried thyme.
Roast the vegetables for 25-30 minutes until tender and caramelized, and roast the chicken for 18-22 minutes until the internal temperature reaches 165°F.
Transfer the roasted squash, onion, and the squeezed-out roasted garlic into a high-speed blender.
Add the chicken bone broth to the blender and process on high until the soup is completely smooth and velvety.
Slice the roasted chicken breast into thin, even strips.
Pour the hot soup into a bowl, arrange the sliced chicken on top, and finish with a dollop of Greek yogurt for added creaminess.