Heat the coconut oil in a large pot or Dutch oven over medium heat until shimmering.
Add the shallots, zucchini, garlic, serrano pepper, and sea salt. Cook, stirring occasionally, for 8 minutes. The zucchini should soften but retain its shape.
Stir in the coconut milk, lime zest, grated ginger, and cane sugar. Simmer gently for 15 minutes, allowing flavors to meld together.
Turn off the heat and let the soup cool slightly.
Transfer the mixture to a blender, then add fresh basil, cilantro, and lime juice. Blend until smooth and creamy.
Taste and adjust seasoning as needed with additional salt or lime juice.
Serve in bowls, drizzling with extra coconut milk if desired, and garnish with fresh basil and cilantro. Serve with lime wedges on the side for added brightness.