Preheat the oven to 400 degrees . Arrange the pita pieces on a baking sheet. Brush with 2 tablespoons EVOO, top with the oregano and crushed red pepper, season with salt and bake until crisp, 10 to 12 minutes.
Preheat a grill pan or cast-iron skillet over high heat. Rub the meat with 1 tablespoon EVOO and season with salt and black pepper. Cook over medium-high heat for 3 to 4 minutes on each side for medium. Let rest for 10 minutes, then slice.
Meanwhile, using a food processor, puree the yogurt, feta, half the lemon juice, the garlic and cumin. If necessary, thin with 1 or 2 tablespoons water.
Layer the lettuce on a platter. In a small bowl, combine the remaining lemon juice, 2 tablespoons EVOO and salt and pepper; pour over the lettuce. Top with the pita, tomatoes, cucumber, red onion, bell pepper, parsley and yogurt-feta dressing. Top with the warm steak, pepperoncini and olives.