1. Combine first 5 ingredients in a Dutch oven; bring to a boil over medium-high heat. Cover, reduce heat to low, and simmer 10 minutes or until vegetables are tender. Cool 10 minutes.
2. Puree vegetable mixture, in batches, in a blender until smooth. Transfer puree to a large bowl; whisk in half-and-half, salt, and white pepper until blended. Let cool 1 hour; cover and chill 4 to 48 hours.
3. Add salt and white pepper to taste. Serve in chilled cups.
We tested with Superior Touch Better Than Bouillon Chicken Base.