Heat oil in a skillet over medium heat. Add shrimp, salt, pepper, and purple onion; sauté 3 to 5 minutes or just until the shrimp turn pink. Remove from heat, add 6 tablespoons Spiced Compound Butter; stir until butter melts.

Divide shrimp, onions, and butter sauce evenly atop squares of cornbread; top each with a dollop of aioli.

Spiced Compound Butter

Combine all spices. Add butter; whisk until well combined. Using a rubber spatula, scrape butter mixture onto plastic wrap; form the butter into a 6-inch log. Roll the log into a cylinder and twist the ends of the plastic so that the cylinder is sealed. Chill at least 2 hours.