How to cook an artichoke? This lovely thistle is a little tricky to cook (if you cook it whole). The reason is that when you put the whole artichoke in the boiling water, it will raise to the surface and a part of it will actually float above the water, making it discolored. To avoid cooking such cameleon artichokes, put something heavy on them while they cook, e.g. a heavy plate. They should stay immersed in the water during the entire cooking process and so their color will remain uniform.