They look kind of thin, so maybe they don't have any batting inside and are just two layers of fabric.
Or maybe have a light fusible backing anyway...

If you notice, the first three all have the same strip sets.....with the second egg pattern turned upside down.
So I bet they just sewed the strips together, cut out the shape, and attached two with like sides together, leaving an opening for turning. Turned, then caught the opening with the double stitched border.

Here are a few tutorials I found. Some are for placemats but just make them smaller for mug rugs.

https://craftyforhome.com/2019/03/25...emat-tutorial/
http://www.2createincolor.com/2013/0...r-egg-mug-rug/
https://cleverlittlemouse.com/easter...emat-tutorial/

If you have an embroidery machine, Anita Goodesign has a selection of those. I made a Candy Corn mug rug for my employees once at Halloween and an Easter Egg another time for another group of employees.

Thanks for the links. One used fusible fleece for the batting. That solved the problem of the batting moving. I've never used fusible fleece. I'll have to check that out.

bkay

I made the first two. I made a strip set, then cut out out the front and coordinating back. I cut the batting a little bit short, then stitched in the ditch to the batting and turned. The first one looked kind of rough to me. Then I looked at the photo and decided that it didn't look that different.

So, I decided to sew across the seams and stitch the border more carefully. I didn't get the second one done, so will take photos when I finish it.

I made them too big for my taste. They finished at about 8.5 X 7. I was kind of going by the sizes suggested by the mug rug swap. If I make anymore, they will be smaller.

bkay