To remove the fibrous stalk base, hold each end of the asparagus spear and bend it gently (A). The spear will break at the place where it changes from tough to tender. Do not cut the stalk ends with a knife.
Using a sharp swivel peeler with a narrow opening, lightly scrape the asparagus spear beginning about 1 in. (2.5 cm) from the tip and gliding the peeler toward the base (B). To keep the spear from breaking, lay it flat on the work surface.