After making what I'm calling an Improv Layered Circle for my Bee Sewcial bee-mate, Leanne/she can quilt, there were several requests for a tutorial. So here was my process for what it's worth!
Lay your circle on your next fabric (called 'fabric 2' going forward) so it's overlapping only by 1/4 or 1/3 of the circle's circumference. Cut along the circle as indicated by the arrows. Discard the bit that was under the circle.
Clockwise from upper left: Flip fabric 2 over onto the circle, right-sides together, and start sewing where the two meet, working up to 1/4" seam as you sew around the curve. Fabric 2 will look bunchy when you are done, but press the circle seam edges out and things will smooth out. Turn over to right side and press again. Click here for a little video of the sewing bit, in case that helps.
Trim fabric 2 so there's a nice curve, starting and ending right at the circle edge. Repeat with your next fabric!
This is a fun technique that really isn't as difficult as the end result might imply. Go slow on the curves, careful not to pull on those bias edges. After a few rounds, evaluate what you've done and trim as needed before continuing on.
I'm anxious to see how you use the technique, so be sure and use the hashtag #improvlayeredcircle if you post on Instagram.