So through what I feel is an admirable amount of trial and error, I worked up what is called a "circular scarf". I deleted pictures of all the steps I had to undo! Here is how to make one that is reversible. Mine has some azn floral print fleece and grey knit fabric.
Here's what you need:
two strips of compatible fabrics, 60" wide by 16"
sewing machine or a tolerance for hand sewing
Take your two strips of fabric and pin them right sides together.
Sew along the long edges, leaving the short edges open.
Turn the tube right side out.
Lay your scarf on a flat surface, folding the ends so the meet in the middle. You're going to put one end into the other to close the circle.
Choose one side to be the female side, or the "receiving side". Fold in a hem of 1/2-1".
Pick up the male end, or the inserting or "pitching" end and lay it on top of the female end so that it overlaps about an inch.
Carefully lift open the female end so the male end falls inside, roughly lining up with the seam allowance on the inside of the female end.
Pin in place, sew up, and wear in as many ways as you can think of.
You can cut your fabric wider for better coverage if you wear it as a hood, but make sure your fabric isn't so thick that it then chokes you when you wear it.