You know, I've never figured out exactly how shrimp steeped in a wonderfully flavorful, spiced butter sauce got the label barbecue, but I don't think anybody's complaining.
A big key is finding the right size of shrimp. Sure, can make this work with any size, as long as you get the sauce right and have lots of French bread for dipping (probably the real star of this dish if we're all being honest). But ideally, you want to start with 16-20 count shrimp, and you also want to leave those heads and shells on. Sure, in a restaurant if you want barbecue shrimp you probably want to skip the whole bib exercise -- because lord knows peeling shrimp coated in butter and spices is messy enough.