These big artichokes are to be eaten cooked ( in contrast with small artichokes who can be eaten raw ). The traditional way to eat them once steamed is pretty simple:
Steam them for 10 minutes in a pressure cooker or 15 to 20 mins in a pot until the leaves are easy to remove. For the vinaigrette, mix some vinegar or lemon, salt, pepper and mustard. One nicely mixed, add some extra virgin olive oil and lightly stir. It’s ready.
You can use the artichokes heart as well in recipes. You can pan sear them or bake them. So many possibilities!
Store in the refrigerator. Eat as soon as possible. Shelf life is 5 to 7 days in the refrigerator, sprinkled with water and sealed in plastic bag. You can freeze artichokes. You need to cook them, sprinkle them with lemon juice to prevent marketing and place them in airtight container in the freezer. They can last 10 to 12 months in the freezer.