Asparagus is a rather pricey vegetable. So I like to make sure that I use as close to every last bit that I can.
But those tough ends can be a problem, just as they are. I do the thing I think we all do, snap the stems to break off the tough ends, then steam or roast the tender parts.
I hang on to the tough ends to use in soups and casseroles. I use a vegetable peeler to remove the tough skin on the those ends. Without the skin, the asparagus ends are tender enough for chopping and adding to casseroles or soup. And the amount of waste is reduced to a small amount of skin from the bottom ends of the stalks.
And I even save the liquid from steaming the long stalks. I pour it into my fridge jar of veggie liquids to add to the next pot of soup. (The liquid in this jar, above, is a combination of asparagus steaming liquid and the liquid from a can of green beans. It was added to a soup that I made on Monday.)
Anyways, I splurged a bit on Sunday, and bought 2/3 pound of fresh asparagus at $1.88/lb, to have with dinner, and I was reminded of peeling the tough ends.