Put the shrimp on a large pie pan or plate and pat them completely dry with a paper towel. Arrange the shrimp so they lay flat and are evenly spaced.
Heat a large skillet over medium heat. Season the shrimp with salt and pepper. Add the butter to the skillet. When the foaming subsides, raise the heat to high, and invert the plate of shrimp over the pan so the shrimp fall into the pan all at once. Cook the shrimp, without moving them, for 1 minute. Add the garlic and cook for 1 minute. Turn the shrimp over and cook for 2 minutes more. Transfer the shrimp to a bowl.
Return the skillet to the heat and pour in the vermouth and lemon juice. Boil the liquid until slightly thickened, about 30 seconds. Scrape up any browned bits from the bottom of the pan with a wooden spoon. Stir the zest and parsley into the sauce. Pour the sauce over the shrimp, season with salt and pepper to taste and toss to combine.
Divide the shrimp among 4 plates or arrange on a platter and serve.