Had it not been for the Online Retreat at our Texas Quilters group I may only have dreamed of it and not actually made it. Seems there is always time to dream and plan but LIFE gets in the way of actually measuring, cutting and sewing. Therefore, we set aside a weekend to do SOME thing toward our projects. It helps me get somethings done, a little or a lot depends on what is going on. Otherwise, who knows if I would have Made the time. Ya Know?
I made a simple template in several sizes for what I call
Faux Cathedral Window along with a sample of what it looks like
here.I realized the middle area was a bit puckered so remedied it on the T'Giving Runner.
When BFF was last in town, we went to the quilt shop sale, half price on fat quarters and we had the best time!
Anyway, I used my templates for the largest Faux Window and laid my fabric out and sandwiched them for a fast cut. As you can see I had lots of help from my Assistant George who is always there to lend a paw.

I like to line up the fabric with the straight of grain so they don't stretch too much during construction. It takes a little more time but is well worth it when you are sewing it all up.

Do the same thing with the big circle, as this is the back of your Faux Window.
Then cut LIGHT weight fusible interface/backing with the square like you did cutting the fabric.
Be careful not to cut your template...I cut my template and it made my pattern a little off because I didn't recut the fabric. I am usually in too much a hurry and don't stop and take my time. NEXT time, I'll do it right...that is my intention, anyway.
Speaking of lending a paw...here is George catching the rolled up webbing for me. Little stinker knows when that camera is on and won't play so I can get good photo.

Once I had the squares and circles cut out it was time to iron on the fusible webbing to the
wrong side of the square. Do them all.

Then begin choosing which squares you want to go with which circles. The beauty and bane of this system is just starting...lol...but try to get lights and darks together making sure you have a nice variety.
OR
You can do all the same like I did in the sample referenced above. I like them both. However, it is less stressful if you use just a couple fabrics.
OR
You can do a traditional white backing as per a Cathedral Window. The options are endless!
Now, lay the square inside the Circle. Make sure the Circle is RIGHT side DOWN and the Square is Right side UP. Like in this photo:

Then Iron them together. The Circle is 1/4 inch wider for a seam allowance. If you want to do this by hand then turn the edge under 1/4 inch and whip stitch it down. I used the machine. IF you choose to hand stitch this part make a sample first so you can see how it is sewing thru the webbing. If it is too difficult, leave the webbing off and pin the square to the circle.

Now your Circles have their Squares attached or pinned. Lay them out on the table or floor and decide what order you want them to be in...took me at least as long to do this as it did to cut out, iron on the webbing, etc.

Now iron the flaps down over the squares. The resulting creases are the sewing line you will use to sew the blocks to each other. You can pin if you like, I found them easy to keep lined up but pinning could also be useful.
You may want to do them by the row or by the individual piece. I did the individual piece due to cutting my template and the Circles being a bit off because of that. It gave a bit of a stretch as the sewing line fell on the bias not the straight of grain. Ordinarily, the ironed seam is to fall right on top of the edge of the square (straight of grain) for the sewing line...I had to ease and hope.

Your options for finishing out the edges of the circle are many. You may turn under the edges of your circles and iron them, if you like, that will make the top stitching faster.
OR
You can use a decorative thread and a stitch on your machine to finish the circles.
OR
You can embellish each seam with a crazy quilt type edge, which would be fabulous if you have the time.
I did a narrow zigzag to anchor the edges then came back over the edges with a wider zigzag.

I like the way it turned out and will post a photo once I get the table cloth on the table for the runner to lay on.