Preheat the oven to 425 degrees F.
Pat dry the chicken and sprinkle it all over with salt and pepper.
Coat a large cast-iron skillet with 1 tablespoon of oil over medium-high heat.
Arrange the chicken thighs, skin side down, in the pan, and place over medium heat. Cook, without moving, until the skin is browned, 14–15 minutes.
Meanwhile, in a large bowl toss potatoes, with pepperoncini, garlic, oregano, remaining oil, salt, and pepper. Set aside.
Flip chicken on the other side.
Add the pepperoncini mixture to the pan, arranging it around the thighs. Pour the brine around the edges of the pan a good shake to evenly distribute.
Transfer the skillet to the oven and cook until the potatoes are tender, 40–45 minutes.
Remove the skillet from the oven and transfer the chicken and peperoncini to a plate.
Place the skillet over high heat and cook potatoes, often stirring for about 4-5 minutes.
Remove from heat and stir in red onion, sliced celery, and parsley.
Arrange chicken and pepperoncini on top of the vegetables, garnish with celery leaves and serve.