Bring large pot of salted water to a rolling boil.
Remove top quarter of artichoke (bread knife works well for this) and trim pointed tips (kitchen sheers work well here) from the remaining leaves. Finally trim the stem to approximately 1/4 inch from the base of the artichoke.
Place trimmed chokes in the boiling water and weigh down with a small plate to keep them submerged. Boil the artichokes until almost ready to eat. Knife should slide in the bottom (stem) with only a little resistence.
Preheat grill to medium-high heat.
Remove from water and drain upside down until cool enough to handle.
Slice each artichoke in half lengthwise. With a spoon, remove the think pinkish leaves and the hairy choke.
In a large bowl, add the oil, garlic salt, juice from limes and oregano and liberally rub mixture onto and into each artichoke half.
Grill each artichoke half turning occasionally until slightly charred, about 8-10 minutes. Serve with clarified butter, your favorite vinaigrette or mayonnaise with a little horseradish and a couple of dashes of hot pepper sauce.