Pat the chicken dry with paper towels. In a shallow dish, season the flour with the salt and pepper. Dredge the chicken in the flour to lightly coat, shaking to remove excess flour, then set aside.
4 boneless skinless chicken breasts, ¼ cup all-purpose flour, ½ teaspoon salt, ¼ teaspoon pepper
Melt 2 tablespoons of the butter in a large skillet over medium heat. Add the sliced apples and onions and season with a little salt and pepper. Sprinkle with the fresh thyme. Cook for 8 to 10 minutes, stirring occasionally so that the apples and onions can soften and brown slightly. The apples should be al dente - not turned to mush but not too crisp still either. Transfer to a second plate and set aside.
3 Tablespoons salted butter, 2 apples, 2 onions, 2 teaspoons fresh thyme
Add the remaining butter to the empty skillet along with the tablespoon of olive oil. Once the butter has melted, place the dredged chicken into the pan and cook over medium heat until lightly browned all over, about 2 minutes per side.
1 Tablespoon olive oil
Add the apple cider and broth to the pan and heat until boiling. Cover, reducing heat to medium-low and simmer until the chicken is cooked through to 160°F on an instant-read meat thermometer, about 8 to 12 minutes depending on the thickness of the breasts.
½ cup apple cider or unfiltered apple juice, ½ cup chicken broth
Return the apples and onions to the pan with the chicken and sauce. Add the cream and stir to combine. Increase the heat to medium-high and cook until the sauce has thickened slightly, about 2 minutes.
½ cup heavy cream
Stir in the cider vinegar and adjust seasoning by adding salt and pepper to taste, if needed. Sprinkle with additional minced fresh thyme, if desired, then serve with the sauce, apples, and onions spooned over the chicken and mashed potatoes on the side.
1 Tablespoon cider vinegar