I decided I wanted to make a brim for my hat for some added ear-warmth, so instead of doing step 9 in the tutorial, I laid the brim part (right side in) under the hat (right side out), and pinned the inner edges together. I then sewed the pinned area together. The photo shows this end product. notice how on the brim, the side seams are facing out, whereas the hat's seams are unseen because they are inside.

Then fold the brim up. The side seams on the brim should now be unseen.

Instead of using black buttons alone for the eyes, I stacked a white button on top of a black button and sewed them on to the brim piece, as you can see in the step 1 photo.
You're done! Enjoy!