Preheat oven to 400 degrees Fahrenheit.
Prepare chicken by trimming off any fat and cut a slit through the center of each chicken breast without completely cutting through the piece of chicken.
Salt and pepper chicken on all sides.
Place thin strips of apple on the inside of the chicken, followed by the pieces of brie. Fold the chicken breast back together.
Heat a non-stick skillet over medium high heat. Add the tablespoon of olive oil. When oil is hot add the stuffed chicken to the skillet. Cook on each side for 2 minutes each just to brown the meat.
Remove chicken from the skillet and place on a baking sheet. Transfer the chicken to the oven to cook through, approximately 20 minutes (use a meat thermometer to check that the internal temperature reaches 165 degrees). Keep the skillet for making the sauce.
When chicken is almost finished cooking, make the glaze for the chicken. Add the shallots to the same pan the chicken cooked in and sauté for 1 minute.
Next add the lemon juice, apple cider vinegar, honey, mustard and cornstarch to a bowl and whisk together to dissolve the cornstarch. Add the mixture to the skillet with the shallots and stir until the mixture begins to thicken about 2 minutes.
Remove pan from heat and return the cooked chicken breast to the pan. Use a spoon or basting brush to cover the chicken with the sauce. Drizzle with a little balsamic glaze if desired. Serve immediately.