Skillet Chicken with Creamy Cilantro Lime Sauce

I made this recipe (with a few my kid friendly adjustments), and it was good.  I did not use the cilantro or red pepper flakes, and I just used dried onion.  You might like it just the way it is.

4 skinless, boneless chicken breasts
1/4 tsp salt
1/4 tsp pepper
1 T olive oil
1 C chicken broth
1 T fresh lime juice
1/4 cup finely chopped onion
1 T chopped cilantro
1/2 tsp red pepper flakes
3 T heavy cream
2 T butter, cubed

Preheat oven to 375.  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 each with salt and pepper. In a large oven-proof 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.)  Set chicken on a plate and cover tightly with foil until later.  Remove skillet from heat and add the broth, lime juice, onion, cilantro, and red pepper.  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 gently, uncovered, for 10 minutes or until the liquid is reduced to around 1/4 cup.  Reduce heat to medium-low, then add the cream and butter.  Stir until butter has melted.  Return chicken to the skillet and place in the preheated oven.  Bake until the chicken is completely cooked through, about 5-10 minutes.  Serve chicken with sauce spooned on top.