With an immersion blender (or food processor), puree the potato mixture just until creamy with some chunks still remaining. It should be a chowder-like consistency.
Add the broccoli to the soup along with the cream. Stir together, cover, and let simmer until the broccoli is tender, about 15 minutes.
Season with salt to taste.
Ladle into bowls and garnish with cheese and chives.
Notes
I buy the florets of broccoli pre-packaged, but if you use the whole broccoli, be sure to separate the florets and discard the tough stem end. Chicken stock has salt, so taste before you add additional salt at the end.
Recipe by Acadiana Table at https://acadianatable.com/2019/01/28/potato-broccoli-soup/