Preheat the oven to 350 degrees F (175 degrees C).

Pat chicken dry with paper towels. Place chicken in a bowl and coat with olive oil. Season liberally with sea salt and black pepper on all sides.

Heat a cast iron skillet over medium-high heat. Add chicken thighs, skin-side down, to the hot skillet. Sprinkle 1 teaspoon za'atar immediately over each chicken thigh. Cook chicken, without turning, until skin is crispy and browned, 7 to 10 minutes.

Turn chicken so skin side faces up and remove skillet from heat. Sprinkle remaining za'atar quickly and evenly over each chicken thigh. Spoon some of the rendered chicken fat from the pan over the top of the za'atar.

Place the skillet in the preheated oven and roast until juices run clear and chicken is no longer pink near the bone, about 15 minutes.