Remove chicken breasts from refrigerator 20-30 minutes before cooking to approach room temperature. Pat thoroughly dry with paper towels. For even cooking, pound thicker portions to create uniform 3/4-inch thickness.
Season chicken breasts generously on both sides with kosher salt, pepper, garlic powder, and paprika if using. Press seasonings gently into the meat.
Place cast iron skillet over medium-high heat for 5 minutes to achieve even heat distribution. The pan is ready when a few drops of water instantly evaporate on contact (approximately 375-425°F).
Add oil and tilt pan to create an even coating. Allow oil to heat until it shimmers but before it smokes—approximately 30-45 seconds.
Place chicken breasts presentation-side down in the skillet. Do not move them for 5-6 minutes to develop proper crust formation.
Once first side is golden brown, flip chicken breasts. Add butter, garlic, and herb sprigs to the side of the pan. As butter melts, tilt pan slightly and spoon the melted butter mixture over chicken repeatedly for 1-2 minutes.
Reduce heat to medium-low, cover skillet with lid or aluminum foil, and continue cooking for 5-7 minutes until internal temperature reaches 160°F at thickest point.
Transfer chicken to a clean plate, tent loosely with foil, and rest for 5-10 minutes. Internal temperature will rise to 165°F through carryover cooking while juices redistribute.