Citrus Vinaigrette

In a large, non-reactive mixing bowl, combine the lemon and lime juices, parsley, and garlic, whisking until well mixed. Very gradually, add the olive oil in a thin, steady stream, whisking constantly until all is incorporated and the mixture looks a bit creamy. Whisk in kosher salt and pepper.
Before using vinaigrette, refrigerate overnight in a covered container to let the flavors develop, then season with more salt if desired. Keep refrigerated and use within 4 days.

To assemble the dish

In a heavy, broad-based saucepan, heat the olive oil over high heat until it is just short of smoking, about 2 minutes. Add the shrimp in a single layer as much as possible, and include any heads that may have come detached. Sprinkle the kosher salt and freshly ground black pepper over the shrimp and, without stirring, cook the shrimp for 1 minute. Reduce the heat to medium-high, and cook the shrimp until pink on both sides, about 3 minutes, turning each shrimp over at least once.
Add 1 1/2 cups of the citrus vinaigrette to the pan. Continue cooking until the vinaigrette just begins to bubble and the shrimp are barely done, about 45 seconds more, moving the shrimp around with a spoon so the vinaigrette flows evenly around the shrimp.
Remove from heat and let the shrimp sit in the pan for about 30 seconds, then pour them into a serving dish and drizzle with the remaining vinaigrette. Garnish with lemon halves.