In a shallow bowl, whisk together extra virgin olive oil, lemon juice, minced garlic, dried oregano, paprika, kosher salt, and black pepper. Submerge the sliced chicken cutlets, tossing to coat evenly. Let marinate for 10 to 15 minutes at room temperature while preparing the salad base.

In a small mason jar or glass measuring cup, combine olive oil, red wine vinegar, lemon juice, Dijon mustard, dried oregano, honey, sea salt, and black pepper. Whisk vigorously or shake for 30 seconds until a smooth, glossy emulsion forms.

Heat a heavy cast-iron skillet or grill pan over medium-high heat with 1 tablespoon of olive oil until shimmering. Place chicken cutlets in a single layer and sear undisturbed for 4 to 5 minutes until deep golden-brown char lines develop. Flip and cook for 3 to 4 minutes more until the internal temperature reaches 165°F (74°C). Rest on a cutting board for 5 minutes, then slice against the grain into thin strips.

In a wide serving bowl, lay down the finely chopped romaine lettuce. Neatly scatter diced Persian cucumbers, halved cherry tomatoes, kalamata olives, thinly sliced red onion, and crumbled Greek feta over the greens. Crown with the warm sliced chicken. Drizzle with the lemon herb vinaigrette, sprinkle with fresh parsley, and toss gently right before serving with warm toasted pita wedges.