How to Make It
Using kitchen shears, cut along the back of each shrimp shell and remove the intestinal vein. In a large saucepan, heat the olive oil. Add the onion, garlic, rosemary and chile and cook over moderately high heat, stirring occasionally, until the onion is softened and just starting to brown, 5 to 7 minutes. Add the beer and simmer until reduced by half, about 5 minutes.
Add the lemon halves, Old Bay and 5 cups of water to the saucepan and bring just to a simmer. Add the shrimp and poach over low heat until just cooked through, 8 to 10 minutes. Using a slotted spoon, transfer the shrimp, onion, garlic and lemon halves to a platter to cool slightly.
Meanwhile, in a medium bowl, whisk the ketchup with the horseradish, lemon juice, Sriracha and Worcestershire.
Serve the shrimp, warm or at room temperature, with the cocktail sauce.