Barbecue shrimp is a Louisiana thing that has nothing to do with barbecue, but thankfully a lot to do with shrimp. Shrimp still in the shell, often with heads on, are served in a sauce of butter, hot sauce, and Worcestershire sauce - a little like a less spicy, more savory Buffalo sauce - so that your fingers get coated with the sauce as you shell and eat the shrimp. French bread sops it up.
When I first moved here, until the supermarket stopped carrying the bread that was ideally suited for it, I used to make "barbecue shrimp poboys" by buying their "demi-baguette" - a sandwich-sized bread with little to do with a baguette except the shape - and then cutting off an end, hollowing it out, stuffed it with boiled shrimp, and pouring in the sauce. It was pretty fucking amazing.
This, though, is barbecue shrimp ddukbokki - Korean rice cakes with Maine shrimp, in a "barbecue shrimp inspired" sauce that starts with stock:
Because I bought a lot of Maine shrimp while they were fresh and cheap, I had a shitload of shrimp shells - no heads, sadly, but plenty of shells - so I made a stock of shrimp shells, dried lobster mushrooms, Old Bay (the seasoning salt), and bay leaves. The idea was to get a savory, umami, shrimpy, bay-y strained stock, pictured here before I cooked it down:
The ricecakes cooked in the stock and a bit of beer until they were supple, with a few dashes of Worcestershire sauce and Louisiana hot sauce; once the ricecakes were nearly cooked, I added the shrimp, continued cooking a couple minutes to cook them through, and then added some cold butter to enrich everything.
My plate had a few added dashes of hot sauce: