Preheat the oven to 425°F (220°C) and line a large sheet pan. Cut the bell peppers, sweet potatoes, and onion into large pieces. Place them on the sheet pan and drizzle 2 tbsp of the olive oil over them.
Slice ⅓ off the end of the garlic bulb so that the cloves are exposed. No need to peel it. Place it on top of a small square of foil and drizzle it with 1 tbsp of olive oil. Loosely wrap it in the foil and put it on the sheet with the cut side up.
Roast the vegetables for 40-45 minutes or until the peppers and onions have some charred ends.
Let them cool down for about 10 minutes. Add the peppers, onions, and sweet potatoes to a large pot over medium-low heat. Let the garlic continue to cool down for now because you will be using your hands to squeeze it.
Add half of the broth, all of the coconut milk, and the seasonings to the pot. Then, use your hands to squeeze the roasted garlic out of the bulb and into the pot. Let this simmer for 10 minutes so the flavors can come together.
Use an immersion blender to purée the soup while it's simmering. (Another option is to use a blender before adding the veggies to the pot.) Stir in the remaining broth and enjoy the soup with your favorite toppings!