Prepare Lemony Moroccan Dip by simply mixing all the ingredients together, then place in the refrigerator while you prepare the artichokes.
Wash the artichokes under cold water and use a sharp knife to carefully cut the top of the artichoke.
Trim away the sharp thistles of the outer leaves- kitchen shears make this easier work- then if your artichokes have a stem, peel with a peeler.
Rub all the cut surfaces with a lemon half.
Steam the artichokes for 20 minutes, remove from the steamer, and let them cool long enough to handle.
Carefully cut the artichokes in half lengthwise, and use a spoon to scoop out the choke.
Brush the artichokes with olive oil and place them on a medium hot grill, grilling for approximately 6 minutes per side.
The artichokes are cooked when the leaves pull away easily; serve with Lemony Moroccan Dip!