Thai Zucchini-Coconut Soup

In a large saucepan, heat oil over medium. Add zucchini, shallots, ginger, garlic, and 2 teaspoons salt; cook, stirring occasionally, until zucchini softens but has not developed any color, 10 to 12 minutes. Add potato, coconut milk, and 2 1/2 cups water. Bring to a boil, then reduce heat to medium-low and simmer until potato is easily pierced with the tip of a knife, 10 to 12 minutes. Remove from heat; let cool slightly. Stir in cilantro and lime juice. Transfer mixture to a blender, working in batches if necessary, and purée until very silky and smooth, 2 to 3 minutes. Refrigerate until cold, at least 4 hours or, in an airtight container, up to 3 days. Season with salt; serve topped with zucchini slices and cilantro leaves.