Cut a horizontal slit through the thickest portion of each breast to form a pocket; divide the cheese evenly among the pockets. Dredge both sides of stuffed chicken breasts in flour that has been sprinkled with salt and pepper.
Heat the oil in a large nonstick skillet over medium-high heat. Add the chicken, and cook 4 minutes on each side or until done. Remove the chicken from the skillet; place on a rimmed baking sheet and keep warm in preheated oven.
MAKE THE APPLE PAN SAUCE:
To a skillet, add the broth, apple cider, and garlic; bring to boil, and cook 10 minutes or until thick and syrupy, stirring occasionally. Add the honey and apple slices, and cook an additional 5 minutes or until the apples are tender, stirring to coat the apple slices with the sauce.
Spoon the apple pan sauce over the warm chicken; garnish with rosemary, if desired.
Notes
If you're not worried about counting calories in this recipe, you can certainly use larger chicken breasts and more cheese.