In a large measuring cup or medium bowl add pitted cherries, balsamic vinegar, garlic cloves, fresh rosemary, and thyme. Juice the orange and add the juice to the large measuring cup then cut the orange halves into quarters and add them to the cup as well. (This will be the sauce)
In a small bowl combine the dried thyme, dried rosemary, garlic powder, and salt to make the seasoning for the chicken.
Lay chicken out on a cutting board and sprinkle one side with the seasoning from the small bowl.
In a cast-iron skillet place olive oil and melt butter over medium heat. Place the chicken breasts seasoned side down into the skillet with hot oil. Season the other side of the chicken. Allow chicken to brown before flipping (3-6 minutes).
Flip chicken and pour contents from the large measuring cup in with the chicken. Drizzle the top of the chicken with honey. Place cast iron into the oven and allow to bake 10-15 minutes. The internal temp of the chicken should be 165 degrees Fahrenheit (75 degrees Celsius).
Remove the cast-iron skillet from the oven, take the chicken out of the pan and let rest for 5 minutes. If the sauce is too thin (see Recipe Notes) simply place the skillet back on the stove bring the sauce to a boil over medium-high heat and cook off some of the excess liquid. It takes only 1-3 minutes. Make sure you watch it closely. If you cook it too long it turns more into a glaze.
Slice chicken and drizzle sauce over the top and serve.
When it comes to the sauce the best way to test it out is to stick a stainless steel spoon in the sauce if it coats and kind of stays on the spoon...slowly running off... your good.