In a medium bowl, combine the chicken with 1 tablespoons of the olive oil, plus the salt, cumin, thyme, garlic, and lemon zest and juice. Let the chicken marinate in the refrigerator for 30 minutes.

In another medium bowl, whisk together the softened feta, yogurt, minced or dried mint and pepper until combined. Set aside or cover and refrigerate until ready to use.

Preheat the grill to medium heat(350F.) or a grill pan on the stove over medium heat.

Grill the chicken over direct heat, covered, until cooked through, about 5 minutes per side. Let the chicken cool for 5 minutes and chop into bite- size pieces.

Meanwhile, brush the lavash with the remaining 2 tablespoons of olive oil. Grill the flatbreads until they are crispy and toasted, 1 to 2 minutes per side.

Spread about 1 cup of the feta mixture over each flatbread and top each evenly with the chicken, herbs, and radish sliced. Garnish with Aleppo pepper and flaky salt, if desired.