Pat the shrimp completely dry with paper towels before you do anything else. This step matters more than people realize, because any leftover moisture will cause the shrimp to steam instead of sear. Once they're dry, toss them in a bowl with the garlic powder, onion powder, smoked paprika, salt, pepper, and a small drizzle of oil until every piece is evenly coated.
Add your remaining oil to a large skillet and heat it over medium-high until it's shimmering and just barely starting to smoke. A properly hot pan is the secret to those crisp, golden edges you want on good sautéed shrimp. If the oil isn't hot enough, the shrimp will release liquid and end up rubbery instead of seared.
Lay the shrimp in a single layer in the hot pan, making sure not to crowd them. Cook for about one minute per side, flipping once the edges turn pink and opaque. Smaller shrimp may only need thirty to forty-five seconds per side, so keep a close eye on them. Work in batches if needed so every piece gets direct contact with the pan.
As soon as each batch is done, move the shrimp to a plate so they don't overcook from residual heat. Shrimp continue cooking for a few seconds even after they're off the flame, so pulling them a touch early keeps them tender. Once all the shrimp are cooked, return them to the pan briefly to warm through together.
Turn off the heat, then toss the shrimp with the sliced fresh basil and a generous squeeze of lemon juice. The residual warmth is enough to soften the basil slightly and release its aroma without wilting it completely. Serve immediately while everything is still warm and fragrant.