Marinate the Chicken: In a shallow glass dish or mixing bowl, whisk together extra virgin olive oil, minced garlic, lemon zest, lemon juice, dried oregano, thyme, cumin, sea salt, and black pepper. Add sliced chicken breast strips and toss until thoroughly coated. Let rest at room temperature for 10 to 15 minutes (or refrigerate up to 4 hours).

Sear Chicken to Golden Perfection: Heat a large heavy cast-iron skillet over medium-high heat with 1 teaspoon of olive oil. Add marinated chicken strips in a single layer without overcrowding. Sear for 3 to 4 minutes untouched until deep golden grill marks appear. Flip with tongs and cook for another 3 to 4 minutes until internal temperature reaches 165°F (74°C) and juices run clear. Transfer to a clean cutting board and rest for 3 minutes.

Warm the Flatbreads: Lightly warm flatbreads or pita rounds in a dry skillet over medium heat for 20 to 30 seconds per side until soft, warm, and pliable.

Assemble & Roll Wraps: Spread 2 generous tablespoons of cool tzatziki sauce down the center of each warmed flatbread. Layer sliced cucumbers, cherry tomatoes, and red onion. Top generously with warm seared lemon herb chicken strips, crumbled feta cheese, kalamata olives, and fresh dill sprigs.

Fold, Slice & Serve: Fold the bottom edge of the flatbread up over the filling, fold in the sides, and roll tightly into a neat burrito-style wrap. Slice diagonally in half with a sharp chef knife and serve immediately!