Now that the cardoon stalk has been pared, cut it into pieces about three or four inches long. As you cut the stalk, more strings and film will peel off.
If you had trouble paring the flat or concave section of the stalk before, you'll find it easier to remove that skin if you cut the stalk form the ribbed side towards the flat side as shown. It's also easier to pare the concave side when working with small pieces of stalk.

