Place cleaned shrimp into a bowl with brine and refrigerate mixture for 20 to 25 minutes. While shrimp are brining, place tomatoes, chili sauce, horseradish, sugar, pepper, and salt in food processor and blend until smooth. Refrigerate cocktail sauce until ready to serve.
Place a baking sheet or broiler pan under oven broiler and preheat for 5 minutes. Rinse the shrimp under cold water and dry on paper towels. In a large bowl, toss shrimp with olive oil and sprinkle with Old Bay seasoning, if desired.
Place shrimp onto a sizzling sheet pan and return to broiler immediately. After 2 minutes, turn the shrimp with a pair of tongs. Return the shrimp to broiler for 1 minute. Transfer to a cold cookie sheet. Refrigerate immediately.