First, prepare the beurre manié by combining the butter and flour using a fork in a mixing bowl. Reserve
Heat a pot over medium heat, melt the butter and toss the onion in and cook for about 2 minutes( you don’t want to colour them). Stir occasionally
Add the garlic, stir and cook for 30 seconds
Toss the broccoli in plus the broth, cover and cook for about 8 minutes
Remove from heat. Using a hand mixer blend the soup.
Put the pot back to low-medium heat and slowly stir in 1/2 cup of cream ( or milk). Give a taste test, add more cream if needed, I usually stick to 1/2 cup.
If the soup is not thick enough for your taste, add about half the beurre manié and stir. Repeat if needed
Adjust seasoning with salt and pepper
Notes
*If you are using cream you shouldn’t need to thicken it.