So we have made these fan before when i first started getting into cookie decorating. I posted some photos here. So glad to see that my piping skills have improved since then :)
Start with the base of the fan, fill the cookie with a flood consistency icing as shown in the picture below.
Let it dry for a few hours and then start piping in the lace details. We use tip #1 and a stiff consistency icing for the lace detail work.