Roast the Vegetables
Preheat and prep: Heat your oven to 400°F (200°C).
Season the veggies: Toss the chopped carrots, sweet potatoes, and onion wedges on a large baking sheet with 1.5 tablespoons of olive oil, salt, pepper, and a tiny pinch of cinnamon. Spread them out in a single layer.
Add the garlic: Tuck the unpeeled garlic cloves between the vegetables so they do not burn.
Roast: Bake for 30 minutes, tossing halfway through, until the carrots and sweet potatoes are fork-tender and show slightly browned, caramelized edges.
Combine and Simmer
Squeeze the garlic: Carefully squeeze the roasted garlic out of its skin and discard the skins.
Warm the broth: In a large soup pot, heat the remaining ½ tablespoon of olive oil over medium-low heat. Add the grated fresh ginger and fry it for just 60 seconds until fragrant.
Merge everything: Add the roasted carrots, sweet potatoes, onions, and squeezed garlic into the pot. Pour in the 5 cups of vegetable broth. Bring to a gentle simmer for 5 to 10 minutes so all the flavors merge.
Blend and Finish
Purée: Remove the pot from the heat. Pour in the coconut milk if you are using it. Use an immersion blender to puree the soup until it is completely smooth and velvety.
Season: Stir in the lime juice. Taste the soup and add extra salt, pepper, or ginger to reach your preferred flavor balance
