Can I cook and eat the flower buds on my cardoon?

Actually you can use the bud and stem leading up to the bud. Just like the artichoke bud the lower part if it has a "hart" and the stem is basically the same stuff as the "Hart" So you can use the leaf stocks, Stems and harts of both Cardoon and Artichoke.

Conventional wisdom is NO! Even the most wonderful Deborah Madison in her fantastic book "Vegetable Literacy" does not address the issue of the flowers. While she devotes a few pages to cardoons, which she says is part of the Sunflower family, she has forever been chasing the unforgettable first amazing taste of cardoons. On p64 she speaks glowingly is eating her first cardoons "in a sforma eaten on a damp December night in Turin. With pieces of the vegetable lodged in a medium of cream, eggs, and Fontina cheese, the dish was absolutely sensational. Ever since that first encounter, I have longed to duplicate it, but after working my way through a case of this gnarly vegetable, I can't say that I have succeeded." Don't feel defeated if you cannot manage them including flowers. Deborah can't then I reckon it can't be easily done or be worth doing. Still she has some wonderful recipes included because she never really gave up her cardoons.

Thanks for the information and the link. :-)

I don't think the flower is edible--I have never seen it in markets or on a menu, and I have spent a lot of time in Italy. I found this discussion on the web, which might interest you: http://forums2.gardenweb.com/forums/load/cornucop/msg061239393340.html