Preheat your oven to 375 °F (190 °C).

If the chicken breasts are uneven in thickness, pound them down to even thickness so they cook through evenly. Sprinkle both sides with the salt and pepper.

In a large oven‑proof skillet, heat the olive oil over medium‑high heat. Add the chicken breasts and cook for about 6‑7 minutes, turning once, until nicely browned on the outside (they do not need to be fully cooked through at this stage). Remove the chicken to a plate and cover loosely with foil; set aside while you make the sauce.

Remove the skillet from heat and add the chicken broth, lime juice, chopped red onion, chopped cilantro, and red pepper flakes. Return the skillet to medium‑high heat and bring to a boil, scraping up the browned bits from the bottom of the skillet. Allow to boil (uncovered) for about 10‑12 minutes, or until the liquid has reduced to about ½ cup.

Reduce heat to medium‑low, then stir in the heavy cream and butter. Stir until the butter is fully melted and the sauce is smooth. Remove the skillet from heat.

Return the chicken breasts to the skillet, turning once so both sides are coated in the sauce. Transfer the skillet (uncovered) to the preheated oven. Bake until the chicken is completely cooked through (internal temperature should reach at least 165 °F / 74 °C), about 5‑10 minutes depending on thickness.

Serve the chicken with the creamy sauce spooned over top. Garnish with extra lime wedges and fresh cilantro if you like.