Remove the large flower buds when they are fully formed but while the bud leaves are still tightly closed to harvest the artichokes for eating. Cut through the stem 3 to 4 inches beneath the bud with a sharp knife to harvest.
Trim off the flower stems completely after the flowers begin to wilt, if you allowed the artichoke to flower instead of harvesting it. Remove the old stem at the point where it emerges from the main plant.
Cut back the entire artichoke plant after the leaves begin to die back following the first few frosts in fall or early winter. Trim off the entire plant to within 12 inches of the ground with sharp shears.
Cover the remaining plant with 12 to 14 inches of soil and leaf mulch after you cut it back. The mulch protects the roots from winter freezing. Remove the mulch in spring as the weather warms and new growth begins.