Preheat your oven to 400°F (200°C). Spread the cubed squash, chopped carrots, and onion on a baking sheet. Drizzle with olive oil, sprinkle with smoked paprika, and toss to coat evenly.
Roast the vegetables in the oven for about 30-35 minutes, until they are deeply caramelized and fragrant, stirring once halfway through for even browning.
Meanwhile, heat a splash of olive oil in a large pot over medium heat. Add the minced garlic and cook until fragrant, about 30 seconds, making sure it doesn't burn.
Once roasted, transfer the caramelized vegetables into the pot with the garlic. Pour in the vegetable stock, then bring to a gentle simmer.
Use an immersion blender or carefully transfer the soup in batches to a blender. Puree until smooth and creamy, with no chunks remaining.
Pour the blended soup back into the pot and simmer for another 5-10 minutes to allow flavors to meld. Taste, then season with salt and pepper as needed.
Serve hot, garnished with a drizzle of olive oil or a sprinkle of fresh herbs if desired. Enjoy the rich, smoky flavor and velvety texture of this seasonal soup.