Preheat the oven to 375°F (190°C).

Pound the 4 chicken breasts to an even thickness using a meat mallet. Season both sides with 1/4 teaspoon salt and 1/4 teaspoon freshly ground black pepper.

Heat 1 tablespoon olive oil in the ovenproof skillet over medium-high heat. Brown the seasoned chicken for 6 to 7 minutes total, turning once with tongs.

Transfer the browned chicken to a plate. Keep the skillet and its browned drippings for the sauce.

Add 1/2 cup finely chopped onion to the skillet and cook for 2 minutes. Add 1 teaspoon minced garlic and stir for 30 seconds.

Pour in 1 cup chicken broth and the juice of 1 lime. Add 3 tablespoons fresh cilantro and 1/2 teaspoon red pepper flakes, scraping the browned bits from the skillet.

Bring the sauce to a boil. Simmer uncovered for about 10 minutes, until it reduces to approximately 1/4 cup.

Reduce the heat to medium-low and stir in 1/4 cup heavy cream. Add 2 tablespoons butter and stir until fully melted and incorporated.

Return the chicken to the creamy sauce and turn each piece to coat. Place the ovenproof skillet in the preheated oven.

Bake uncovered for 5 to 10 minutes, until the chicken reaches an internal temperature of 165°F (74°C). Spoon the cilantro lime sauce over the chicken before serving.

Continue to boil gently, uncovered, for about 10 minutes or until the liquid is reduced to around 1/4 cup.

Turn heat to medium-low, then add the cream and butter.

Stir until butter has melted and is well incorporated.

Add chicken back to the sauce, flipping it to coat it in sauce.

Add cheese to the top of the chicken if desired.

Place the whole skillet in the preheated oven and bake uncovered until the chicken is completely cooked through, about 5-10 minutes.

Serve chicken with sauce spooned on top.