I like to use a kitchen scissor to cut only the very bottom from the stalk; breaking it off causes more of the bottom to go to waste, which is otherwise perfectly edible. With the smaller, thinner "pencil" asparagus, the stalks are too thin to peel and you need that protective layer so the asparagus keep their shape during cooking. For larger asparagus, where the skin is tougher, I do peel the stalk but leave the tip and an inch or so below the tip, unpeeled. The top is tender enough that it can be cooked as is.
Properly seasoning the boiling water is crucial; it should taste like mild seawater for the asparagus to absorb flavor. The ice bath is essential for stopping the cooking process quickly and preserving the vibrant green color and crisp-tender texture (al dente). Thoroughly drying the blanched asparagus before dressing is arguably the most important step. Excess water dilutes the vinaigrette and prevents it from clinging properly to the stalks, significantly diminishing the flavor impact. For larger asparagus, peel the tough lower skin but leave tips unpeeled.