Add potatoes, broth, water and spices to the pot and boil until broccoli stems are tender. About 20-30 minutes. Note: if using beans instead of potatoes, do not add them yet.
Puree the soup base with an immersion blender or pour into a blender (carefully) to puree and then transfer back to the stockpot. Note: if using beans, puree 1 can of the beans and then add the other can whole.
Add broccoli florets and simmer with the lid on (this gets thick and bubbly) for about 8-10 minutes until florets are tender.