Heat your broiler on high (450°F) with an oven rack set 6 inches from the heating element (not directly below but the second rack from the top). Line a rimmed, broiler-safe baking sheet with foil (for easy cleanup).
Pat the shrimp dry with paper towels. Place them in a large bowl.
Add the olive oil, kosher salt, smoked paprika, garlic powder, and cayenne. Toss to coat with a large spoon.
Arrange the seasoned shrimp in a single layer on the prepared baking sheet. If there's any remaining olive oil mixture in the bowl, spoon it evenly on top of the shrimp, as shown in the video below.
Broil the shrimp until opaque and cooked through, 6-7 minutes for jumbo shrimp, and 5 minutes for large shrimp.
Video
Notes
There's no need to flip the shrimp midway through cooking. You can broil them undisturbed until they're fully cooked.
I don't recommend using frozen shrimp in this recipe. If yours are frozen, you can quickly defrost them by placing them in a large bowl, covering them with cool water, and replacing the water once or twice. They should be defrosted after about 5 minutes in the water. Drain them on paper towels before using them.
You can keep the leftovers in the fridge, in an airtight container, for up to three days. Gently reheat them in the microwave, covered, at 50% power, or add them cold to a salad.