We had the first killing frost last night, and today, I need to cut down my asparagus plants. Sever stems to about six inches from the ground and mulch with 4-5 inches of pine needles. Before discarding the vegetation into the compost pile, check for praying mantis cocoons; this beneficial insect tends to attach its egg masses on side shoots. Remove the cocoon without disturbing the casing and store under a overhang or protected area away from possible predators.
For artichoke plants – cut limp vegetation a couple of inches from the ground, heap a good amount of pine needles against the base of the stems and place a netting or branches to keep the mulch from blowing away.
Another way is to eradicate the plant, place in a container filled with damp sand and store in the basement or garage until spring.
Nick Mancini, The Organic Italian