Hi Katherine -- I'm a newbie on this site. My mother-in-law lent me a quilted casserole carrier recently. I can't upload a pic for you right now but I'll describe it here and upload a (very amateur) drawing.
Basically it's two long strips of quilt sandwich (say 18 inches x 9 inches). One is laid out north-south and the other east-west, one on top of the other. Where the two strips sit on top of the other, a wooden base is inserted and sewn in. (You could also use a square cork mat.)
The east-west sides will come over the casserole dish sides and they stick together with velcro.
The north-south sides each have three pieces of fabric sewn to the ends, through which you put a length of dowel. Those are the handles.