Pat the shrimp dry on both sides with paper towels. Place them in a large bowl. Add the olive oil.
In a small bowl, mix the salt, pepper, smoked paprika, garlic powder, ground cumin, dried thyme, and cayenne pepper. Add the spice mixture to the shrimp.
Toss with a large spoon to coat the shrimp with the oil and spices.
Heat a large 12-inch skillet over medium-high heat. Add the shrimp in a single layer. Use a rubber spatula to transfer any residual oil and spices from the mixing bowl to the skillet.
Sauté the shrimp until cooked through, about 2 minutes per side. I use two spoons to flip them.
Transfer the shrimp to a serving platter. Drizzle them with the pan juices, garnish with chopped parsley, and serve.
Video
Notes
Don't overcook the shrimp. Two minutes per side over medium-high heat should be enough for large shrimp.
Make sure the shrimp are completely dry before cooking them. If they're fresh, place them on paper towels to drain them. If you've defrosted them overnight, run them under lukewarm water to get rid of any residual ice, then place them on a double layer of paper towels, in a single layer, to dry for 10 minutes. Any extra moisture will cause them to steam instead of sautéing and dilute the spices' flavor.
If you'd like to lower the sodium content, you can use just ½ teaspoon of Diamond Crystal Kosher Salt. The sodium per serving will be reduced to 1046 mg.
You can keep the leftovers in the fridge in a shallow, airtight container for up to three days. Reheat them gently in the microwave at 50% power, or use them cold in salads, lettuce wraps, or served with cocktail sauce.