I had 9 of these blocks done and put off for months doing the outside. Doing set-in circles is a bear and it never comes out perfectly. I have watched Sharon Schambers' videos and realized I could use the Piece-le-que technique for this.
Use a sheet of the heat-resistant mylar plastic and cut finished circle size out of the middle. Lay plastic over the fabric and trace the circle. Cut out the circle with a generous seam allowance and clip the curve all around. Pin the plastic over the wrong side of fabric so it stays in place, pinned into a pressing board. Use a brush to paint the seam allowance with starch. Turn the edges back around the plastic, iron dry, and remove the plastic. Place the cutout circle over the center, lining it up all around, pin, and use Elmer's School Glue to attach it, using a very fine tip for a tiny line of glue. Iron to set. Open it up and sew right on the pressed line. Trim the seams. It came out just perfect!!