Artichokes are a bit of a faff to prepare, but once you’ve tasted the results you’ll realise it was worth it!  Once you’ve braised the artichokes, instead of putting them in a gratin you could add them to a salad instead, or marinate them in herbs and olive oil and serve them cold as antipasti.  How much of the artichoke you cut away and how much you save to eat totally depends on the artichoke’s size and maturity.  Cut off anything that you imagine will still be tough after cooking.