How to Make It
In a large saucepan, heat the 2 tablespoons of olive oil. Add the onion and garlic and cook over moderate heat until translucent, about 8 minutes. Stir in the thyme and bay leaf and cook until fragrant, about 1 minute. Add the sliced zucchini, season with salt and cook, stirring occasionally, until tender, about 10 minutes. Add the water and bring to a boil. Remove the saucepan from the heat. Discard the bay leaf and stir in the shredded basil.
Working in batches, puree the soup in a blender until very smooth. Transfer the zucchini puree to a large bowl. Stir in the ice. Refrigerate the zucchini soup for at least 3 hours, until thoroughly chilled.
Season the soup with salt and pepper. Ladle into shallow bowls and top with a small handful of purslane and zucchini shavings. Drizzle with olive oil and serve.