Preheat your oven to 400°F (200°C). Spread the peeled and chopped sweet potatoes and carrots on a baking sheet. Drizzle with olive oil and toss to coat evenly.
Roast the vegetables in the oven for about 30-35 minutes, until they become tender and lightly caramelized around the edges. The aroma will be warm and inviting.
While the vegetables roast, peel and finely mince the fresh ginger. Measure out the smoked paprika and set both aside.
Transfer the roasted vegetables into a large pot. Add the minced ginger, smoked paprika, and vegetable broth. Bring to a gentle simmer over medium heat.
Allow the mixture to simmer for about 10 minutes, letting the flavors meld and the ginger infuse the broth. Season with salt and pepper to taste.
Use an immersion blender to blend the soup directly in the pot until smooth and velvety. Alternatively, carefully transfer the mixture to a blender and puree until silky.
Return the blended soup to a gentle simmer if needed. Taste and adjust seasoning with more salt, pepper, or a dash of lemon juice for brightness.
Serve the hot soup in bowls, garnished with a sprinkle of paprika or fresh herbs if desired. The soup will be thick, vibrant in color, and bursting with roasted, spicy, earthy flavors.