trim the cut side to match the uncut side like above
Stitch each side of your seam down, this will give a nice finished look on the outside of the hat as well as making it less lumpy on the inside.
Use a piece of scrap fabric roughly 2 -1/2 inch by 1-1/2 inch and fold sides in 1/4 of the way, them fold in half (just like quilt binding or bias tape). Stitch around edges. Fold ends in 1/8 inch and stitch to hat, this leaves an opening so you can hang your hat on a hook as well as giving it a little flair.