Put the butter in a large pot over medium heat. When it melts, add the leek, season with salt and pepper, and cook, stirring frequently, until soft, 4 to 5 minutes. Add the garlic and cook for 1 minute more.
Add the peas and 6 cups water. Bring to a simmer and cook until the peas are soft, about 5 minutes. Add the mint and basil and cook until herbs are wilted, about 3 more minutes. Remove the pot from the heat, and purée the soup with an immersion blender.
Once the soup has cooled somewhat, pour it through a fine metal strainer placed over a large bowl, and press with a spatula to extract as much liquid as possible. Discard the solids.
Refrigerate the soup for at least 4 hours or overnight. When ready to serve, season carefully with salt and pepper to taste and stir to combine. Serve in chilled bowls and garnish with a small mint leaf and drizzle of lemon olive oil, if desired. (Store leftover soup in an airtight container in the refrigerator for up to several days.)
