Preheat your oven to 200°C (390°F) and line a large baking sheet with parchment paper.
Peel and chop sweet potatoes and carrots into even chunks, then toss them with olive oil, smoked paprika, a pinch of salt, and pepper. Spread them out in a single layer on the baking sheet.
Roast the vegetables in the oven for about 30-35 minutes, until they are tender and caramelized around the edges. The aroma will be sweet and smoky.
While the vegetables roast, chop the onion and mince the garlic. Heat a tablespoon of olive oil in a large pot over medium heat, then sauté the onion until translucent and fragrant, about 5 minutes.
Add the minced garlic to the pot and cook for another minute until fragrant.
Once the roasted vegetables are cool enough to handle, add them to the pot with the sautéed onion and garlic. Pour in the vegetable broth and bring the mixture to a gentle simmer.
Simmer the soup for about 10 minutes to allow flavors to meld, then remove from heat.
Use an immersion blender to carefully purée the soup directly in the pot until smooth and creamy. Alternatively, transfer small batches to a blender, then return to the pot.
Stir in the coconut milk for added creaminess, then squeeze in fresh lemon juice. Taste and season with salt and pepper as needed.
Let the soup sit off the heat for a few minutes, then give it a final stir. The soup should be velvety, warm, and inviting with a slight sheen on top.
Serve hot, garnished with a drizzle of olive oil or fresh herbs if desired. Enjoy your cozy bowl of roasted sweet potato and carrot soup!