Preheat oven to 400F.
In a large skillet, heat 2 tbsp of butter over medium-high heat.
Once hot, add in all of the sliced onions, apple slices, and 1/2 cup apple cider. Cook for 15-20 minutes or until browned and softened.
While onions and apples are cooking, pound chicken breasts with mallet or roller until even and thinner that before. Around 1 inch thick all around.
Season both sides of chicken with thyme, salt, and pepper.
Set finished onions aside in a bowl. Add remaining 2 tbsp of butter to skillet and then add chicken.
Sear chicken for 5 minutes on each side. Once it has been seared on each side, set chicken aside on a plate.
In a small bowl, mix together remaining 1/2 cup apple cider and 1/2 cup chicken broth with 1 tbsp arrowroot powder.
Add onions back to skillet over medium-low heat, along with the broth arrowroot mixture. Whisk together for 2-3 minutes or until thickened. Turn off heat.
Add chicken back to skillet and using a spoon, cover the chicken with the onions, apples, and sauce. Add thyme sprigs around chicken.
Transfer skillet to oven and bake for 8-10 minutes or until internal temp reads 165F.
Sprinkle with parmesan and remove thyme sprigs.