3 pounds large shrimp, shelled and deveined, tails left on
Salt and freshly ground pepper
1 cup extra-virgin olive oil
1/2 cup fresh lemon juice
1/4 cup coarsely chopped dill
3/4 cup water
Warm pita bread, for serving
Season the shrimp with salt and pepper and cook in 3 batches: For each batch, heat 1/3 cup of the olive oil in a large deep skillet. Add one-third of the shrimp and cook over high heat, turning once, until golden, about 3 minutes. Add 2 tablespoons of the lemon juice and 1 tablespoon of the dill and toss to coat, then transfer the shrimp as it's cooked to a large deep serving platter. Add 1/4 cup of the water to the skillet and boil over high heat, scraping up any browned bits from the bottom of the skillet, until the juices are reduced to 2 tablespoons; add to the cooked shrimp.
Add the remaining 2 tablespoons of lemon juice and 1 tablespoon of dill to the shrimp and season with salt and pepper. Toss well. Serve the shrimp warm or at room temperature, with the warm pita bread.
The cooked shrimp can be refrigerated for up to 3 hours. Bring to room temperature before serving.