Place chicken breasts between two sheets of plastic wrap and pound to an even 3/4" thickness. Pat dry thoroughly with paper towels.

In a shallow dish, combine olive oil, 1 teaspoon finely chopped rosemary (from one sprig), 3 minced garlic cloves, salt, and pepper. Coat chicken evenly and allow to rest at room temperature for 20-30 minutes.

Place cast iron skillet on medium-low heat and allow it to heat gradually for 5 minutes.

Increase heat to medium-high. Add butter and allow it to melt and begin foaming. Immediately place chicken breasts presentation-side down in the pan.

Cook undisturbed for 5-6 minutes until a golden-brown crust forms.

Turn chicken using tongs. Add remaining whole rosemary sprigs and lightly crushed garlic cloves around the chicken. Reduce heat to medium.

Cook for an additional 5-7 minutes, occasionally tilting the pan and basting the chicken with the infused butter-oil mixture.

Use an instant-read thermometer to verify chicken has reached 165°F (74°C) at its thickest point.

Transfer chicken to a plate and tent loosely with foil. Allow to rest for 5 minutes.

While chicken rests, add 2 tablespoons stock or wine to the skillet, scraping up browned bits. Allow to reduce by half, then drizzle over chicken before serving.