Heat oven to 400° F. Place a rimmed baking sheet in the oven.
Rinse the chicken and pat it dry with paper towels. Using your fingers, carefully loosen the skin from the meat. Tuck some of the parsley and 1 slice of garlic under the skin of each breast. Season both sides of the chicken with the salt and pepper.
Warm 1 tablespoon of the oil in an ovenproof skillet (preferably cast-iron) over medium-high heat. Add half the chicken to the skillet, skin-side down, and cook until golden, 5 to 6 minutes. Transfer the chicken to baking sheet. Repeat with the remaining oil and chicken. Roast until the skin is crisp and the chicken is cooked through, about 25 minutes. Let rest for 5 minutes. If desired, serve the chicken with any pan juices.
In Advance: Place the garlic and parsley under the skin of the chicken breasts and season with the salt and pepper. Cover and refrigerate for up to 24 hours before cooking.