Meanwhile, in 4 quart heavy bottom pot bring oil to medium heat, sauté onion and carrot until golden and softened, then add garlic and sauté an additional 5 minutes.
Add all seasonings.
Add broth, bring to gentle boil and add potato.
Remove broccoli from water bath and trim the outer most ends of the florets, almost like shaving the broccoli.
Reserve this in a bowl.
Chop the remaining broccoli and add into the boiling pot.
Allow to cook for 5-10 minutes, just until tender.
Then, remove the pot from heat, use an immersion blender or scoop the soup into a blender.
Blend until smooth.
Return to pot and heat.
Add cream and cook on low for 5-10 minutes, then add trimmed florets and cheese, stir to fully combine.
Serve hot.