Excuse me if this was your idea and I've unknowingly borrowed it, but I had about three bunches of asparagus bottoms in my fridge. I snap them and let them break where they want naturally, usually about three quarters of the way down and I make the asparagus as a vegetable and save the woody bottoms until inspiration hits.
I have been a pressure cooker kick lately so I cooked about three bunches worth of woody stems with plenty of water and some sal mixteca for about 30 minutes on high pressure. After a quick release, I tool the asparagus out and worked it through a food mill, leaving rich delicious liquid below and all the woody fiber in the mill.
In a soup pot I sauteed some onions and garlic in a little olive oil and once soft, added a spoonful of dried porcini mushroom powder from the Wine Forest. This made a thick paste. Then I added the liquid from the pressed asparagus and about a cup of leftover bean broth from a pot of Ayocote Morados I had in the fridge.
Obviously you can use a different bean or omit it all together. I love the porcini powder but you could omit it and maybe add some soy sauce of fish sauce or nothing. If you don't have a food mill, you could push the puree through a sieve,, using the back of a wooden spoon to help but for my kind of cooking, I find I use a food mill a lot. I've tried something similar with an immersion blender but there's little worse than fibrous strings ruining an otherwise velvety soup.
The bigger point is many people through away their bean broth and woody vegetable waste but I was able to make it into several swell meals.