First I'll start off saying this is very rich, and should you be on a diet I wouldn't suggest this one.
At Costco you can get a 3 LB bag of just broccoli stems.
I started with 4 cans of chicken broth and added one chopped white onion and some garlic salt & pepper into my 6qt roaster . Simmer that until onions are soft.
Then dump in the whole bag of broccoli, cover and let it get all soft, falling apart. Use a potato masher to smoosh into teeny bits.
To that I put a cubed up 2LB box of Velveeta and 1/2LB of grated cheddar. Let that melt. Poured in 1 quart of 1/2 & 1/2. Salt and pepper to taste.

This made a lot of soup, but you can cut it in 1/2 or whatever. It freezes great!