Heat the coconut oil in a large pot or Dutch oven over medium heat. Add the shallot, zucchini, garlic, serrano, and salt and cook, stirring occasionally, for 8 minutes, or until the zucchini is soft but not mushy. Add the coconut milk, lime zest, ginger, and sugar and simmer for 15 minutes. Turn off the heat and allow to cool slightly.

Transfer the soup to a blender and add the basil, cilantro, and lime juice. Blend until smooth and season to taste.

Pour the soup into bowls and drizzle with more coconut milk, if desired. Garnish with basil and cilantro and serve with lime wedges for squeezing.