My wonderful friend Robyn made these for me. I love them, they make me happy. She used a Freshcut fabric charm pack. I love that fabric line! What's really fun is they are different fabrics on each side, so I continuously flip them to show new fabric. I'm going to take the liberty of guessing how these are made.
Take two squares right sides facing, sew around the edges, leaving an unsewn portion in order to turn it right side out. Turn, press. Topstitch all the way around the edge. Then, starting on the outside edge, topstitch in a 1/4" square spiral all the way to the middle. Did I miss anything, Robyn?
Postscript: Robyn says she used some cotton batting in between the squares also, and that the idea for the coasters came from Joelle Hoverson's Last Minute Patchwork & Quilted Gifts. Thanks again, Robyn!