The warts get removed, anyway. I was reminded of that old riddle: What do you eat that you have more of when you're done? Which really applies to big artichokes. With the baby ones, I slice off the top and most of the stem, remove the tough outer leaves and use a vegetable peeler on the stem.
Then I cut them in half and sauté them in butter over low to medium heat until they are just this side of burnt. I usually have to add more butter halfway through. With truly baby artichokes (as opposed to these teenagers), you may not need to cook them as long.
If you have regular access to them (lucky!), you could steam them or boil them and put them in salads and such. But they are so rare for me that I just cook 'em up and eat them all by themselves. Just like that.