Boil covered for 30 minutes, adjusting the heat as needed to maintain a medium boil ().Uncover, and transfer artichokes using tongs to a colander to drain, stem side up. This little blog’s for all you folk wondering how to wrap your mouth around this … Cook Artichokes: Add artichokes to a large pot (), add water until they start to float, and cover.Bring to a boil over high heat. Globe artichokes should have tightly packed, firm heads with no brown patches on the outer layers. How To Cook & Eat Globe Artichokes on December 12, 2019. Globe artichokes (Cynara scolymus)… They’re a strikingly beautiful plant to grow and, when starting out, strikingly confusing to eat. Young globe artichoke buds can be cooked and eaten whole.