In a large cast iron skillet or heavy-duty pan, heat the remaining olive oil over medium high heat. Place the chicken leg quarters, skin side down, into the skillet. Arrange the foil-wrapped bricks on top of the chicken quarters so that the bricks are pressing down on all of the chicken.
Cook, pressing down on the bricks occasionally, for 20 to 25 minutes, or until the skin is crispy. Remove the bricks, turn the chicken over, place the bricks back on the chicken and continue cooking for about 5 minutes more until chicken is cooked through. Chicken is done when it feels firm to the touch and a meat thermometer inserted in the center reaches 180 degrees F. Remove the chicken from the skillet to rest.