Preheat your oven to 400°F (200°C) and line a baking sheet with parchment paper.
Toss the cubed squash and carrot chunks with 2 tablespoons of olive oil, ensuring each piece is lightly coated. Spread them out evenly on the prepared baking sheet.
Sprinkle the vegetables with toasted ground cumin and smoked paprika, then use your hands or a spatula to mix and coat them evenly with the spices.
Roast the vegetables in the oven for about 35-40 minutes, stirring halfway through, until they are tender, caramelized, and slightly charred at the edges.
Transfer the roasted vegetables to a large blender or use an immersion blender in the pot you plan to serve the soup from.
Add the vegetable broth to the blender, then blend until the mixture is smooth and velvety. Alternatively, use an immersion blender directly in the pot, blending until creamy.
Pour the blended soup into a pot, bring to a gentle simmer, and season with salt and pepper to taste. Let it cook for about 10 minutes to meld the flavors.
Taste and adjust seasoning as needed. If the soup is too thick, stir in a splash of warm broth until desired consistency is reached.
Serve the soup hot, optionally garnished with a drizzle of olive oil or fresh herbs for extra aroma and color.