One of my earliest favorite food memories is of a time when my grandfather was babysitting my brothers and me and he introduced us to raw broccoli stems. I'm not sure if he brought the broccoli over to our house, or my mom just had some in the fridge. There is this particularly vivid memory of him slicing up the stem and salting the pieces. Not sure if I was thrilled about vegetables at the time (I was probably 10 or 11). I probably enjoy eating broccoli stems more now than I do the heads.
The technique is simple: slice raw broccoli and gently season with salt and/or pepper. The trick is to remove all the tough parts with a sharp knife or vegetable peeler. I like to "square up" the stem with my knife, removing all the tougher darker green parts. The interior is tender and much lighter in color. You can slice however you like; I generally prefer cutting them into matchsticks. They are also very good dusted with Tajin or chili powder.
Did you know that broccoli heads are actually immature flower primordia? Each bud will turn into a flower and then eventually produce seeds.