Heat olive oil in a large saucepan over medium heat. Stir in onion, carrot, and celery; cook and stir until the onion has softened and turned translucent and the vegetables are tender, about 5 minutes.
Pour in chicken stock and rice; bring to a boil. Cover, reduce heat to low, and simmer for 35 minutes or until rice is soft.
Stir in spinach, lettuce, and parsley; cook just until wilted. Season with salt, black pepper and cayenne pepper. Use an immersion blender (or blend in batches in a blender) until smooth. The soup may be thinned with more broth, if desired. Refrigerate overnight before serving. Garnish as desired.