Pour in the vegetable broth and bring to a gentle simmer. Add the fresh or frozen peas and cook for 3 to 5 minutes until bright green and tender.
Remove the pot from the heat. Stir in the fresh mint leaves, coconut milk, sea salt, and black pepper.
Use an immersion blender to puree the soup directly in the pot until smooth and creamy. Alternatively, transfer the mixture in batches to a stand blender.
Return the blended soup to low heat just to warm through. Taste and adjust seasoning if necessary. Serve warm or chilled, garnished with extra fresh mint leaves.