1. Preheat oven to 500 degrees . Heat a 10-inch cast-iron skillet over high heat. Divide dough into four pieces and stretch each one to roughly the size of the skillet. Add 1/2 teaspoon oil to skillet, swirling to coat, and put in one piece of dough. Cook 1 minute, then flip and bake until brown and crisp, about 5 minutes; set aside. Repeat with remaining dough.
2. Meanwhile, using a blender or a hand blender, puree 2 tablespoons oil, garlic, anchovies, yogurt, lemon juice, mustard and 1/4 teaspoon pepper.
3. Return skillet to burner over high heat. Toss chicken with remaining oil and season with salt and remaining pepper. Cook, flipping once, until golden and cooked through, about 4 minutes.
4. Slice chicken into 1/2-inch pieces and toss with romaine and dressing in a large bowl. Divide among pizzas and sprinkle with Parmesan.