Preheat broiler to high. Line a rimmed baking sheet with parchment or foil.
Place tomato halves cut side up on the prepared baking sheet. Brush the tops of each half with olive oil, and sprinkle with kosher salt and black pepper. Broil on high until soft and slightly charred in spots (10 to 15 minutes) and let cool.
Add tomatoes, grated horseradish root, bottled horseradish, lemon juice, Worcestershire, Tapatio, honey, and 2 pinches of salt to a food processor. Pulse several times until the mixture is slightly smooth -- there should still be some texture left. Season to taste with additional kosher salt, black pepper, or lemon juice.
To serve, place a small bowl of cocktail sauce on a plate and pile cooked shrimp around. Garnish with parsley leaves.
Kitchen Konfidence is a collection of recipes and techniques aimed to inspire the home cook to do more in the kitchen.
About Brandon: I enjoy cooking with seasonal ingredients, making ice cream and shaking up some killer cocktails. When I am not cooking and taking pictures of my food, I am at the beach, carousing with friends, taking day trips up the 5, or engaging in all manner of computer geekery.