You need:
37″ x 15 1/2″ main fabric for scarf
37″ x 15 1/2″ contrast fabric for scarf
10″ x 7 1/2″ main or contrast fabric for the band

Cut out the fabric for the scarf body and the band.

Right sides facing, pin the long sides together, leaving the ends open.

Using a 5/8″ seam allowance, sew both long sides of the scarf. Press the seam. Now you have a long tube.

Finish your seams using your method of choice. Here we used an overlock stitch on the sewing machine. You can try a zigzag stitch, serging the edges or simply cutting the edges with pinking shears.

Turn to the right side. Press the seams again.

Fold the scarf in half so that the ends are on top of each other. Pin the seams together through two layers, leaving the out the contrast fabric.

Pin along the contrast fabric.

You are pinning along the inside of the tube. In order to sew this, you'll need to leave about a gap. Place a pin 3" from the seam line in the contrast fabric (shown in white). Do this at the bottom seam line as well. You'll have a small gap in your contrast fabric.

Because of the unpinned gap, you're able to pull out the pinned section. It looks like a seashell.

Start sewing at the first pin on the main fabric. Back tack. Continue sewing onto the contrast fabric and back onto the main fabric. If you are able to push the fabric through a little further, do so. Be careful not to stitch through more than two layers of fabric. Back tack when you finish the seam.

Now you still have a seashell, except it’s been sewn. See how the body of the scarf is coming out of that small opening? That’s exactly what you want.

Snip the threads. Begin to push the seam you just sewed into the scarf, pulling the main fabric around it.

There will be a hole a few inches long on the side of the main fabric.

Match seam allowances on the inside and pin in place. Hand sew across using a slip stitch.

The seam is closed all the way around the cowl now. If there’s any puckering, don’t worry because it will be concealed by the band.

Time to make the small band! Pin the sides of the band together, right sides facing each other.

Sew up the sides. Pull the fabric through to the right side. Press the seam into the middle of the band.

At one end of the band, push the fabric in about 5/8″, forming a crisp edge. Iron it flat.

Place the band beneath the scarf, centering it over the seam. Pinch the scarf as you pull the band around it.

Push the unfinished edge of the band into the finished end about 5/8″, so one is encasing the other. Pin in place.

Here you can either slip stitch both sides or stitch through all layers. Here we used the slip stitch on both sides. Slip stitching all around produces a clean finish. Tack the band to the scarf.