These are only about two inches across, but as last year's artichoke season went on long enough for the kids to be quite sick of them, I figured we might as well start this year when the first buds were young and chokeless.
I used to just pull off the outer leaves and boil them 'til they were soft. Nowadays I prefer to boil them in acidulated water (add a tablespoon of lemon juice or vinegar) until just tender, then slice in half and dig out whatever choke there is with a narrow spoon. (The smaller ones in the strainer above had no choke at all - I almost could have eaten them whole). Then I place the halves in a baking dish, drizzle with olive oil, sprinkle with coarse salt, and place under the broiler for a minute or two.