Pat the shrimp dry. Moisture is the enemy of a good sear. Lay shrimp on paper towels and pat until no surface moisture remains.
Season with salt, pepper, a pinch of dried oregano, and smoked paprika.
Make the dressing. In a small bowl, whisk together olive oil, lemon zest, lemon juice, red wine vinegar, minced garlic, dried oregano, red pepper flakes, 1/2 teaspoon salt, and several grinds of black pepper. Taste and adjust acidity or salt.
Prep the vegetables. In a large bowl, combine tomatoes, cucumber, red onion, olives, roasted red peppers, parsley, and mint. Toss with half of the dressing so the flavors start to mingle.
Cook the shrimp. Heat a large skillet over medium-high.
Add a light drizzle of olive oil. Cook shrimp in a single layer for about 1.5–2 minutes per side, just until pink and opaque. Do not overcook.
Assemble the salad. Add cooked shrimp to the vegetable bowl.
Pour in the remaining dressing and toss gently. Fold in crumbled feta.
Serve over greens. Place arugula or mixed greens on plates or a platter. Top with the shrimp mixture.
Finish with a crack of black pepper and an extra squeeze of lemon if you like.
Optional bulk-up. If using quinoa or farro, spoon the salad over 1/2 cup cooked grains per serving to make it extra filling and even higher in protein.