I love to grill and love my smoked pulled pork. Also love shrimp. This combines smoke with shrimp. I like to use a grilling skillet, but feel free to use skewers. Adapted from a Steven Raichlen recipe. Prep time does not include the time to soak the wood chips. Shrimp marinating time is included in prep time.
To prepare shrimp, combine paprika and the next 9 ingredients (through red pepper). Combine olive oil and shrimp in a bowl, and toss to coat. Sprinkle shrimp with rub, and toss to coat. Cover and refrigerate 30 minutes.
To prepare rémoulade, combine mayonnaise and the next 10 ingredients (through garlic) in a medium bowl. Remove yolks from eggs; discard yolks or reserve for another use. Finely chop egg whites, and stir into mayonnaise mixture. Cover; chill.
Remove grill rack, and set aside. Prepare the grill for indirect grilling, heating one side to high and leaving one side with no heat. Pierce the bottom of a disposable aluminum foil pan several times with the tip of a knife. Place pan on hot coals on the hot side of grill; add soaked wood chips to pan. Let wood chips stand for 15 minutes or until smoking.
Place grill rack on grill. Place shrimp in a grilling skillet (or use skewers); place skillet on grill rack over unheated side.
Cover and grill 15 minutes or until shrimp are done, stirring after 7 minutes. Serve with rémoulade.