The raw broccoli stalks are pretty tough and fibrous but they are edible and very healthy. The trick is to make sure they are sliced or chopped in small pieces so they aren't tough to eat. Use a vegetable peeler and shave off some of the outer part of the stalk. Then there are so many ways to use it.Add finely chopped broccoli stalks in soups and vegetable slaw. You can use very thinly sliced stalks in a stir fry or a salad. Also cut off about 1/4 inch of the bottom stalk. And then you can thinly slice the bottom into round "coin-like" shapes and roast in the oven.