Build a fire in your oven and bring temperature to 500 degrees. Close oven door to maintain temperature. Generously salt and pepper your chicken all over.
Heat the olive oil in a large cast iron skillet over medium heat. Remove from heat then carefully place chicken pieces in skillet, skin-side down. Place the double foil-wrapped bricks on top of the chicken.
Place skillet inside oven. When you open the oven door, the temperature should fall quite a bit. You want the overall temperature to hover around 475 degrees for this.
Roast chicken for 15 minutes, rotating skillet midway through.
After 15 minutes, CAREFULLY remove the bricks and flip the chicken. Place bricks back on chicken and return to the oven. Roast for 15 more minutes (again, rotating midway through).
Remove bricks and add the figs to the skillet. Return skillet to the oven for just 4 minutes so the figs start to caramelize.
Remove skillet and let the chicken and figs rest.
Drizzle the balsamic on the arugula with a pinch of salt. Place chicken and figs on this and pour the pan juices from the skillet over everything. Finish with an extra pinch of salt and serve.
This dish can easily be modified for the barbecue. Just make sure your grill stays around 475 degrees and roast in the skillet with the top on the grill.