My new favorite! Tastes like it includes cheese, but it doesn't!
Melt butter with olive oil in a large pot over medium heat. Careful not to let get too hot or smoke!
Add onions, broccoli stems, and carrots to heated butter and oil. Stir over medium heat until carrots are tender and onions are translucent.
Add broccoli florets and stir for about 2 to 3 minutes.
Add flour and stir all together for about 1 minute. Make sure to stir constantly!
Add chicken stock and bring all to a boil. Lower heat, cover, and let simmer for about 15 to 20 minutes, stirring occasionally.
Add cream, then blend in portions in blender (Be careful not to overload blender - it will splash out the top!) or with a stick-blender (Remove from heat first and be careful of spurting hot liquid!)
Return to low heat for about 2 to 3 minutes; serve immediately or chill, reheat, and serve the next day.