There are 2 separate issues with asparagus, was it cut at its prime and has it been cut recently. Freshly cut or at least cut and stored properly spears should be crisp and firm, not rubbery. Asparagus cut at its prim should have tight tips to the spears. As it ages the tips will start to open up. Size of the spears is not related to the age of the stalk, it is not zucchini.
Ah, you attached a photo as I was typing. I would cut the bottoms and maybe peel the thicker ends too, but don't toss those peelings! https://food52.com/blog/16564-peel-asparagus-fry-the-trimmings
Perhaps you meant to attach a picture to show us? In any case, you might find this guide helpful: https://food52.com/blog/19472-a-guide-to-cooking-every-asparagus-from-the-straggly-to-the-chunky
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