Artichoke after Harvest

I grew an artichoke plant in Mississippi. No one around here knows anything about them. After harvesting my artichokes, 21 large buds in all, I cut the large stems back as low as I could, which left only a dozen or so of the very large old leaves. They look terrible and I see no new signs of growth. Looking under the mulch I see vigorous root growth. What should I do, cut it back all the way to the ground? The plant is about 8 inches in diameter at ground level