Whisk the flour and chicken stock together; set aside
Chop up the carrots, celery and green onions.
Heat the olive oil in a large stockpot over medium heat. Cook the carrots, celery and green onions for about 6 minutes, until the vegetables are tender-crisp.
Add the flour/chicken stock mixture and the broccoli to the pot.
Turn the heat up to medium-high, the mixture to a boil. Then, turn the heat down low and simmer for about 10 minutes until the broccoli is soft.
Stir in the half-and-half
Use an immersion blender to blend the soup until it is smooth.
Stir in the shredded cheddar cheese and black pepper