Preheat the broiler to high with a rack set 3-inches from the heat source.
Toss the shrimp and asparagus with 1/4 cup ketchup, 2 tablespoons horseradish, oil, 1/4 teaspoon salt and a few grinds of pepper. Spread out on a rimmed baking sheet in one layer and broil, stirring once or twice, until the shrimp are just cooked through and lightly charred in spots along with the asparagus, about 6 minutes.
Stir together the remaining 1/3 cup ketchup, the remaining tablespoon horseradish, the sour cream, lemon juice, and 3 tablespoons water. Stir in half of the parsley.
Put an iceberg wedge on each of 4 plates and divide the shrimp and asparagus evenly among them. Drizzle with the dressing and sprinkle with the remaining parsley. Serve with lemon wedges on the side.
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