Preheat your oven to 400°F (200°C). Toss the cubed sweet potatoes and sliced carrots with 2 tablespoons of olive oil and the smoked paprika until evenly coated. Spread the vegetables in a single layer on a baking sheet and roast for about 25-30 minutes, until tender and slightly caramelized.
While the vegetables roast, heat 1 tablespoon of olive oil in a large pot over medium heat. Add the minced garlic and sauté for about 1 minute, until fragrant and just beginning to turn golden.
Remove the roasted vegetables from the oven and add them to the pot with the garlic. Pour in the vegetable broth, bringing the mixture to a gentle boil.
Use an immersion blender to blend the soup directly in the pot until smooth and creamy. Alternatively, carefully transfer the mixture to a blender in batches, blending until silky, then return to the pot.
Season the soup with salt and pepper to taste. Adjust the spices, adding more smoked paprika if you desire a deeper smoky flavor.
Bring the soup to a gentle simmer for 5 minutes to meld the flavors, stirring occasionally and watching for a velvety, vibrant orange appearance.
Once ready, taste and adjust seasoning as needed. Serve hot, garnished with fresh herbs or a drizzle of olive oil if desired.
