Preheat the grill to medium heat.
In a large bowl, prepare the brine by mixing ice, water, sugar, and kosher salt until dissolved. Add the shrimp and let them soak for 25-30 minutes.
In a mixing bowl, combine crushed garlic, diced tomato, jalapeño, brown sugar, Asian chili sauce, horseradish, red wine, Old Bay seasoning, hot sauce, and corn starch to create the cocktail sauce.
Transfer the cocktail sauce mixture to a saucepan, bring it to a boil, then reduce to a simmer and cook for 8-10 minutes.
Grill the shrimp using skewers, a griddle, or a steamer tray for 1-2 minutes per side until charred and cooked through.
Plate the charred shrimp and generously spoon the cocktail sauce over them.