Melt 1 Tbsp. butter in a large, non-stick skillet over medium-high heat. Add the apples and saute until softened. Set the pan aside.
Tuck a slice of Brie and several slices of apple into the pocket on the underside of the chicken breasts between the breast and the tenderloin. Season the chicken with salt and pepper. Pat a little flour onto both sides of each chicken breast.
In the skillet, melt 1 Tbsp. butter over high heat. When the butter foams add the chicken breasts and brown them on both sides. Transfer the chicken to a cooking sheet, stuffed-side-down, and put it into the oven for 15 minutes. While the chicken is cooking, make the sauce.
Pour the cider and broth into the skillet and boil it over high heat until reduced to about 1-1/2 cups. Swirl in the remaining 2 Tbsp. of butter. Season to taste with salt and pepper. To serve, divide the chicken among 4 plates and pour a little sauce over each.