I've never had persimmons. We bought some the other day, but we haven't tore into them yet. I have no idea the best way to eat them. My wife seems certain, but she's been too busy to prepare them.
So I stare at them on the countertop, looking like little weird tomatoes. Soon, my little persimmons, soon.
This is about the most difficult to eat Dutch delicacy I can think of:
When you press down on the top, the cream in the middle comes out.
Looks like a clear case of "Eat with your fingers" to me.
If it's anything like the vanilla slice* it resembles, then using hands is the way to go but you're still going to have the same problem, but you can then rotate it to get at the filling that's come out.
* There seem to be two main kinds of vanilla slice in Australia - the "real" kind, which features a stiff, yellow vanilla custard in between two pieces of puff pastry, topped with passionfruit icing (or occasionally something heretical like the pink icing in the photo), and the "French vanilla slice", also known as a Napoleon, or a mille-feuille, which usually has an extra middle layer of pastry, a whiter, creamier custard, and is topped with either icing sugar or a kind of streaky mix of white and chocolate icings.