Heat the oil and saute the onion a few minutes. Add the chicken broth and bring to a boil. Add the broccoli and turn down the heat to a simmer and cook 8 minutes, stirring now and then. If you want smooth soup, like we like, use an immersion blender to blend it up.
Stir in the cheese and sour cream and warm through. Do NOT a boil. Taste and season with salt and pepper as needed.