The tough ends of asparagus, for example, can be used for soup. When asparagus is in season and inexpensive, I buy a lot of asparagus. Sometimes I'll save all the tough ends for soup. Those ends have a lot of fiber, which is why you trim them off. But they've also got a lot of flavor, and a little bit of edible fiber-free vegetable matter.
Normally, I cook those ends to soften them, then pass them through a food mill to get rid of most of the fibers, then through a strainer to get rid of the last bits. It's a lot of work.
When I got a juicer to test and review, I decided to see what it would do with asparagus ends. I cooked them as usual (I should have tried them raw, too, but I didn't) and then ran them through the juicer. I ended up with about a cup of juice and pulp.
If you don't have a juicer, you can run the cooked stems through a food mill instead. Or press it though a strainer. If you still have a lot of fine fibers, run it though a fine strainer.
This is also a great use for left over asparagus.
Cream of Asparagus Soup
2 cups milk
About 1 cup asparagus pulp
1/2 teaspoon salt (more to taste)
Hint of nutmeg
1/4 teaspoon paprika
Several grinds white pepper
Peel the potatoes and cook in salted water until tender. Drain the water and mash the the potatoes. Add the milk and asparagus; heat just to a light simmer. Add the salt, just the barest grind of nutmeg (it's a strong flavor -you want just a tiny amount) the paprika, and the pepper.
Taste for seasoning and add more salt, as needed.
Serve hot or chilled.
A garnish of asparagus tips looks pretty. A sprinkle of cheese or a squirt of lemon juice would also be interesting..