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Heat the oil in a Dutch oven or large saucepan. Add the onion, celery, and garlic and cook for 5 minutes.
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Add the thyme, paprika, and cauliflower. Stir, cook for 5 minutes and add the broth and water.
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Bring to a boil, reduce heat to a simmer and simmer for 10 minutes, or until cauliflower is tender.
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Add the chicken to the pot. Using either an immersion blender or regular blender, puree the soup to desired consistency, leaving pieces of chicken if desired. Serve hot.