Heat the olive oil in a large pot over medium-high heat. Add the onion, celery, carrots and Cajun seasoning and cook, stirring occasionally, until the vegetables are slightly soft, about 4 minutes.
Stir in the quinoa, then add the chicken broth, 3 cups water, 1/2 teaspoon salt, and pepper to taste. Partially cover and bring to a simmer, then reduce the heat to medium and cook until the quinoa starts to soften, about 12 minutes. Add the broccoli and cook, uncovered, until just tender, about 5 minutes. Add the chicken and stir to warm through. Season with salt and pepper.
Ladle the soup into bowls. Top with the sour cream and Cajun seasoning to taste.
Recipe courtesy Food Network Magazine