Carefully remove the skin with a sharp knife, keeping it fully intact, then set it aside for later use.
With the knife, butterfly the breast, making shallow cuts until it's splayed out in a uniform thickness, in a rectangle-ish shape. Cover breast with plastic wrap and pound with a meat mallet until it's about 1/2" thick. Season with salt and pepper.
Mix stuffing and brie, and spread over the top of the breast, leaving a 1" border around the edges, then roll from one short end to the other. Stretch the skin over the seam to seal it.
Secure it with a few pieces of butcher twine, then rub all over with the butter. Season with a little more salt and pepper.
Bake at 350 degrees for 45-60 minutes, until it reaches an internal temp of 165 degrees (I use a digital meat thermometer), then let rest about 10 minutes before cutting. Reserve the pan drippings for your gravy.
Top with chopped parsley and gravy and serve.