There are some additional ideas for using broccoli stems in these two articles: https://food52.com/blog/8140-tara-duggan-on-root-to-stalk-cooking and https://food52.com/blog/9431-eat-all-your-vegetables-how-to-use-stems-and-roots

One year in college, I lived in a household of Chinese students. They would cut them up for stir fries and wonder what to do with the leftover florets.

I too love the slaw...

Broccoli cole slaw! Delicious!

The stems are fabulous for making Broccoli Soup - either cream of or puree. They're actually the best tasting part of the broccoli.

I like to poach them in cream along with slices of fresh horseradish and carrots, them purée and season them and serve as a base for roasted meats or grilled vegetables.

Peel them, cut them in coins, Soak them in vinegar, salt, water and red pepper flakes over night or a couple of days. Then drain them a bit and eat garnished with sesame seed oil.

They are my favorite part. Peel the woody exterior off with a veg peeler or knife. Slice into coins or any shape you want. Roast, grill or steam and toss with butter.