Thaw the shrimp. Leave them in the refrigerator overnight.
Pat the shrimp dry.
Peel them to allow smoke to get inside.
Set the Smoker to 225 degrees F.
While it’s warming toss the shrimp with oil, basil, and garlic.
For better protection from burning, wrap the smoking grate with aluminum foil.
Use a fork to poke holes in it to let the smoke through.
The shrimp need 30 minutes to smoke, during which time you can dab compound butter every 20 minutes.
Eat right off the grill.