Cut the peeled cucumber in half length-wise. Using a spoon, scoop out and discard the seeds. Cut the cucumber into roughly 1 inch chunks. Peel and pit the avocado. Cut flesh into 1 inch chunks.
In a food processor or blender, add the cucumber, avocado, cilantro and scallion. Pulse until the mixture is roughly chopped.
Add the broth, yogurt and lime zest and juice and continue to purée until smooth. Season with salt and pepper to taste and chill for 4 to 6 hours.
If using, quarter tomatoes and drizzle with olive oil. Add to soup before serving, as garnish.