Preheat the oven to 420º F and line a small baking tray with parchment paper. Slice ¼ inch top part of the garlic head off leaving cloves exposed. Drizzle garlic and tomato with 1 teaspoon of olive oil and roast for 25 minutes. Remove from the oven and let garlic and tomato cool on a counter.
Heat the remaining olive oil in a large pot over medium heat. Add onion, carrot, ¼ teaspoon of salt, and sauté until vegetables have softened, about 7 minutes. With a slotted spoon, transfer vegetables to a plate.
In the same pot melt vegan butter. Add butternut squash and sauté for 5 minutes. Pour in 3 cups of vegetable broth and cook on a medium-low heat for 20 minutes, or until squash is tender.
Add onion and carrot back into the pot along with paprika, cumin, cayenne pepper and the remaining ½ teaspoon of salt. Peel roasted tomato, slice it in half, remove the seeds and roughly chop. Squeeze the garlic pulp out of its skin and add it along with the tomato to the soup. Cook everything for 5 more minutes.
Using an immersion blender, puree the soup. If soup is too thick to your liking, add ½ - 1 cup of broth. Add coconut milk and heat through. Adjust the seasoning if necessary and remove soup from the heat. Ladle soup into bowls and serve.