Sprinkle chicken breasts evenly with sea salt (approximately 1/2 teaspoon per breast). Place on a wire rack over a sheet pan and refrigerate, uncovered, for 2 hours to dry brine.
Preheat oven to 425°F and position rack in middle position.
In a small bowl, combine chopped rosemary, thyme, and parsley with 1 tablespoon olive oil to create a paste.
Remove chicken from refrigerator and pat dry thoroughly with paper towels. Coat completely with the herb mixture, pressing gently to adhere.
Heat a cast iron skillet over medium-high heat. Add avocado oil and heat until shimmering but not smoking.
Place chicken breasts presentation-side down in the skillet and sear undisturbed for 3-4 minutes until a golden crust forms.
Flip chicken breasts, then transfer the skillet immediately to the preheated oven.
Roast until the internal temperature reaches 160°F at the thickest part (approximately 8-12 minutes depending on thickness).
Remove from oven and transfer chicken to a cutting board. Tent loosely with parchment paper and rest for 5-7 minutes. The temperature will rise to 165°F through carryover cooking.
Slice chicken against the grain and drizzle with remaining tablespoon of olive oil before serving.