Pat chicken dry and make a pocket in each chicken breast by slicing horizontally into the breast and cutting without going all the way through to the back or sides. Season both sides of the breasts with salt and pepper, as well as inside the pocket.
Divide the brie slices between the two pockets, stuffing them inside, along with 3-4 thin slices of apple. Optionally, you can seal the pockets with toothpicks.
In a large skillet over medium-high heat, heat the olive oil and butter. Add the chicken and sear until well browned on both sides, about 2 minutes per side. It should not be cooked through at this point. Transfer the chicken to a plate and cover to keep warm.
Return the pan to medium heat, add the onions and cook for 2-3 minutes until softened. Add remaining apple slices, season with a pinch of salt, and cook until apples and onions are lightly browned, about two minutes more.
Add the wine to the pan to deglaze. Use a wooden spoon or silicone spatula to scrape the browned bits up from the pan. Reduce the wine by half.
Sprinkle flour over the apples and onions and stir until no white streaks remain, about 1 minute.
Stir in the chicken broth, maple syrup, cider vinegar, mustard, and rosemary. Bring the sauce to a boil, then reduce to low and simmer for 5 minutes. Taste the sauce and season with salt and pepper to taste.
Add the chicken back to the pan, along with any juices from the plate. Cover the pan and simmer until the chicken is cooked through, about 8-10 minutes longer. Chicken should register 165F on a meat thermometer. Remove the rosemary sprigs and serve.