There are several YouTube videos on facing a quilt. Basically you are using 4 strips of fabric on top of your quilted piece like a frame. The outline you want is sewn through the strips and the quilt front. The outline is then trimmed with pinking shears or with small snips along the edge to ease the turning and so you can manipulate the edge until it lays nice. The straight edge of the facing strips are then hand stitched to the back of the quilted piece.
You could do the same thing by laying a solid piece over the front, do your fancy edge, cut a chunk out of the center and turn it right side out. The problem with that is, it uses more fabric and you have the hole in the back to either cover with a label of turn the edges under by applique method.