I got a bit ambitious with seeds and have several plants starting out!
Cut off the tops they are edible. They are just another thistle. Tear out the strings which you can't really digest. Bake with butter, parmigiano and perhaps bread crumbs. You should be able to coax some artichoke like flavor out of them.
there are quite a number of traditional French dishes with cardoons. I had the chance to work with them last winter in Lyon (France). Be sure to wear gloves when you are handling them or your hands will turn black. (voice of experience). and it's really hard to get that color out from under your fingernails!