Spray 12 wooden toothpicks with nonstick spray; set aside.
In a small bowl, combine apple, cheese, bread crumbs, 1 teaspoon thyme, lemon juice, 1/4 teaspoon salt and 1/4 tsp. pepper.
On a cutting board, lightly press each chicken breast flat with one hand; using a sharp knife, carefully cut a horizontal pocket (do not pierce top, bottom or far side of breast).
Divide the apple mixture into 4 portions and stuff into each chicken pocket. Pin close with prepared toothpicks. Sprinkle the remaining salt and pepper over the breasts.
Dredge chicken in flour to lightly coat; tap off excess flour.
Heat oil in a large nonstick skillet over medium-high heat. Add chicken and brown 3 minutes per side.
Pour 1⁄2 cup of apple cider and the chicken broth into skillet; Sprinkle with remaining 1/2 teaspoon of thyme. Bring mixture to a boil; reduce heat to low, cover and simmer 5 to 7 minutes until chicken is cooked through and stuffing registers 165 degrees on an instant-read thermometer.
Remove chicken to a serving plate; cover with foil to keep warm. Whisk in mustard and remaining 1⁄4 cup cider into juices in skillet; boil mixture 3 minutes on high until reduced and slightly thickened. Spoon sauce over chicken and serve.