To butterfly giant shrimp, arm yourself with small sharp-pointed scissors, and start cutting at the large end of the outside curve of the shell, cut through the length of the shell down to the beginning of the tall, see illustration. Then, with a knife, cut through the length of the flesh just to but not through the underside of the shell. Remove the intestinal vein.
Whisk the marinade ingredients in a large mixing bowl; fold in the shrimp. Cover and refrigerate for an hour or two, basting the shrimp with the marinade several times.
Drain the shrimp and wipe them off with paper towels. (Reserve the marinade in a small bowl, beating in a little extra oil.) Open the shrimp flesh side up; push one skewer through the large ends to hold them open, and another near the tall end if needed. Or you can use a longer skewer for several shrimp.
To Grill - Set flesh side down close under the red-hot broiler element for 1-1/2 minutes-, turn, brush with marinade, and broil flesh side up another 1 to 2 minutes or so, depending on size, basting once or twice.
To Barbecue - Start flesh side down; turn, baste, and finish flesh side up, basting once or twice.