Cauliflower: throw in food processor/blender and grind them good.
Broccoli: wash, and chop into small chunks.
Mushroom, celery: slice thinly.
In a small sauce pan with cover, add chicken/vegetable stock and broccoli, simmer for 10-15 minutes until broccoli is almost at desired tender.
With your soup pot on medium heat, add butter, wait for butter to be melted then add garlic.
When garlic is golden, add mushroom, celery, onion and carrot. Stir and season them a bit with 1/2 tsp salt and 1 tsp dijon. Stir well to mix.
Now add the cream, pureed cauliflower, chopped broccoli w/ broth.
Stir well and bring the pot to boil.
Then reduce heat to low and simmer for 5 minutes with stirring in between.
Add the shredded cheese and stir well over low heat until cheese is fully mixed in.
Keep stirring until thicken and remove from heat.