Combine carrots and onion in a soup pot with the oil; cook over medium heat, just until vegetables soften.
Add 2 cups chicken broth, tarragon, and white pepper, reduce to low, simmer slowly for 10 minutes.
Put mixture into food processor and process until pureed, then pour back into soup pot.
Add 2 additional cups of broth to the soup pot, then stir in the rice over medium heat and stir, cooking until heated through.
Serve hot with a dollop of sour cream on top of each serving.