Rather than composting your broccoli stems, chop them into smaller chunks (raw) then pulse in a food processor - instant broccoli rice! You can cook it in a pan over medium heat and season as you would cauliflower rice or
I peel mine with a vegetable peeler and put them in the steamer with the rest of the broccoli. I cook the hearts of cabbage also in a steamer and put a tiny bit of butter salt and lemon pepper