Warm 1 tablespoon butter in a large, nonstick saute pan over medium-high heat. Add the apples and saute until softened. Set the saute pan aside because you'll need it again. 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 saute pan, warm 1 tablespoon butter over high heat. When the butter foams add the chicken breasts and brown them on both sides. Transfer the chicken to a sheet pan, stuffed side down, and put it into the oven for 12 to 14 minutes.
While the chicken is cooking, make the sauce. Pour the cider and broth into the saute pan and boil it over high heat until reduced to about 1 1/2 cups. Swirl in the remaining 2 tablespoons of butter. Season to taste with salt and pepper.
To serve, divide the chicken among 4 plates and pour a little sauce over each.