In a large saucepan over medium-low heat, combine the ketchup, garlic, 1 cup of water, hot sauce, brown sugar, Worcestershire sauce, soy sauce, Cajun seasoning, paprika, and the red, white, and black pepper. Salt to taste. Allow the mixture to simmer for around 30 minutes.
Once the mixture is done simmering, place the cornstarch and 1 tablespoon of water into a small bowl. Stir until the cornstarch has dissolved. If needed, you can add more water to fully dissolve all of the cornstarch. Stir the cornstarch mixture into your saucepan and continue simmering for 15 more minutes.
Next, stir your butter into the sauce mixture. Simmer the mixture until the butter has melted and the sauce has thickened, approximately 15 minutes.
Once your sauce has finished simmering, it is ready to be enjoyed!