Set your oven to 375°F and prepare a baking sheet with parchment paper or grease a broiler-safe skillet.
Slice each chicken breast horizontally to create a pocket, taking care not to cut all the way through, then sprinkle salt and pepper inside.
Arrange thin apple slices inside each chicken pocket, layer with thin slices of cold brie, then fold the chicken closed to encase the filling.
Place the stuffed chicken breasts onto the baking surface and bake for 25 to 30 minutes until nearly cooked through.
While the chicken roasts, combine apple cider or juice, maple syrup, garlic, dijon mustard, fresh thyme, and salt in a small skillet and simmer over medium heat until the liquid reduces by half and thickens, about 12 to 15 minutes.
Switch your oven to broil, brush the maple glaze generously over the chicken breasts, then broil for 10 to 12 minutes until the chicken reaches 165°F internally and the glaze lightly caramelizes; watch carefully to prevent burning.
Serve the chicken hot with extra maple glaze drizzled on top for a flavorful finish.