So I found a tutorial that is not paper pieced and tried it.
I used two different hand dyed fabrics for the inner section. (Hand dyed by Vicki Welsh) I really love the brown and the shibori pieces. Then I used a couple of charm squares for the other section. I don't think I made good color/value choices as the inner square "bleeds" into the brown corners. But, this is why you should make test blocks - you learn from them. I should have used the brown for the outer corners. However, it was fairly easy to make and it came out at an unfinished 5 1/2 inches - just as planned.
The tutorial is at Red Pepper Quilts - just click on that and it will take you right to it. These are a great block to use for fussy cutting fabric motifs for that center section. And it you alternate "light, dark, light" or "dark, light, dark" as you do the rounds, this block will really pop.
Here are a couple of drawings to show what I mean.
|light, dark, light|
|dark, light, dark|
Of course, that center can be a fussy cut, just let the background be the appropriate dark or light for maximum value pop.
Now, I suggest doing a couple of these "the slow way" (just the one block at a time.) Then you should be able to line up your cut pieces and chain piece away at these. That will save you the time of jumping from the sewing machine to the iron to the cutting board and back to the sewing machine four times for each block.