Pat the shrimp dry. Moisture is the enemy of good searing. Use paper towels to dry both sides, then season lightly with salt, black pepper, and the paprika.
Heat the skillet. Place a large skillet over medium-high heat. Add 2 tablespoons olive oil and let it shimmer.
Sear the shrimp in batches. Add half the shrimp in a single layer.
Cook 1–2 minutes per side until just opaque and lightly golden. Transfer to a plate. Repeat with the remaining shrimp, adding a bit more oil if needed.
Sauté the garlic and chili. Reduce heat to medium.
Add the remaining 1 tablespoon olive oil, then the garlic and red pepper flakes. Cook 30–45 seconds, stirring, until fragrant. Do not let the garlic brown.
Deglaze with wine. Pour in the white wine and scrape up any browned bits.
Let it bubble for 1–2 minutes to reduce slightly.
Add tomato and lemon. Stir in the diced tomato, lemon zest, and half the lemon juice. Simmer 1–2 minutes to soften the tomato.
Finish the sauce. Swirl in the butter (if using), parsley, oregano, and capers. Taste and adjust with salt, pepper, and more lemon juice if needed.
Return the shrimp. Add the shrimp and any juices from the plate.
Toss to coat and warm through for 30–60 seconds. Don’t overcook—shrimp should be just firm and juicy.
Serve immediately. Drizzle with a little extra-virgin olive oil. Spoon over your favorite base or serve with warm bread to soak up the sauce.