dansch wrote:Low 'n slow would be my approach - shrimp that thick will get tough and chewy on the outside before the insides are done cooked over direct heat. I'd probably poach or sous vide cook them until just underdone throughout, blasting on the grill briefly to brown and set a glaze/sauce/whatever.
-Dan
I've worked with shrimp of unusual size (SOUSes?) before and Dan speaks the unfortunate truth: they get tough. The ones I've had before also had something of a muddy flavor. I would exercise the same caution as you might when cooking, say, spiny lobster - for heaven's sake, don't let it get rubbery.
I hope these monsters are delicious -- do let us know how they turn out!