Preheat the broiler to high. Place the tomatillos in a large skillet and transfer to the oven. Broil for 3-5 minutes, turning halfway through cooking until the tomatillos begin to char all over. Remove from the oven and reduce the oven temperature to 400 degrees F. Transfer the tomatillos to a blender. Add the diced green chiles, garlic, chili powder, and a pinch each of salt and pepper. Pulse until just combined and a sauce forms. Slice the chicken through the middle horizontally to within a 1/2 inch of the other side. Open the two sides and spread them out like an open book. Stuff the cheese and few poblano pepper slices inside and then close like a book over the filling. Place the chicken in the skillet. Add the remaining poblano pepper and drizzle both lightly with olive oil. Sprinkle with salt and pepper. Transfer to the oven and bake for 10 minutes. Add the tomatillo sauce and continue baking for another 10 minutes or until the chicken is cooked through. Serve with rice or tortillas. Enjoy!