Add all ingredients, except shrimp and garnishes to a large saucepan on high heat. Bring to a boil for 10 minutes. Reduce the heat to low. Add the shrimp and cook until bright pink, about 5 minutes. Drain the shrimp from the cooking liquid and place in a serving dish. Chill or eat while warm, sprinkled with the dry rub before serving alongside Cocktail Sauce.
Neelys BBQ Seasoning:
Add all ingredients to a bowl and stir until combined. Keep in an airtight container for up to 6 months.
BBQ Cocktail Sauce:
Mix all ingredients in a small bowl. Cover and refrigerate until use.
Neelys BBQ Sauce:
In a large saucepan, combine all ingredients. Bring mixture to a boil, reduce heat to a simmer. Cook uncovered, stirring frequently, for 1 hour 15 minutes.