Coat the leg quarters with lemon-pepper, salt, and parsley. Let sit in the refrigerator, covered, for 2 hours.
Preheat the oven to 400 degrees F (200 degrees C).
Heat olive oil in a skillet over medium-high heat. Sear chicken, skin-side down, to help crisp the skin, about 5 minutes per side. Transfer to a roasting pan.
Bake in the preheated oven until no longer pink in the centers and juices run clear, about 1 hour. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).