How do I make a caramel disk?
You can freeze caramel, but I don't think that is your best option. I think your best option is to pour the caramel while it is still warm enough to pour into equal sized disks, and let it stiffen naturally. Use a silpat or a lightly greased surface.

To do so would take some practice, but once you have it down, you should be able to do it pretty easily and with very little waste.

If you have the dexterity, you could even pour the slightly warm caramel right onto the cookies.