Preheat oven to 375°F (190°C).

If the chicken breasts are uneven in thickness, pound them down so they’re all even. This way all the breasts will cook through simultaneously. Sprinkle both sides with salt and pepper.

In a large ovenproof skillet, heat the oil over medium-high heat. Add the chicken and cook for 6–7 minutes, turning once. You want the chicken nice and browned on the outside. (It doesn’t have to be cooked all the way through yet.) Transfer chicken to a plate and cover with foil until step 5.

Remove skillet from heat and add the broth, lime juice, onion, cilantro, and red pepper flakes. Return to heat. Cook and stir to scrape up the browned bits from the bottom of the skillet. Bring to a boil. Allow to boil, uncovered, for 10-12 minutes or until the liquid is reduced to 1/2 cup. Reduce heat to medium-low, then add the cream and butter. Stir until butter has melted, then remove from heat.

Add the chicken back to the skillet, turning once to coat both sides in the sauce. Transfer the skillet to the preheated oven. Bake uncovered until the chicken is completely cooked through, about 5–10 minutes (internal temperature should be at least 165°F (74°C)).

Serve chicken with sauce spooned on top, and garnish with lime wedges and cilantro, if desired.

Leftovers keep well in the refrigerator for a few days. You can reheat on the stove over medium heat, in the microwave, or in the oven.