I would like to make a thin disk of caramel that could be placed on the top of a cookie. I need it to be very smooth with neat edges because I plan to cover it with royal icing. I was wondering if I made a chewy caramel recipe, but spread it thin, freeze it, then cut with a round cutter, would that work? I've never frozen caramel before, so I don't know if it would have any adverse effects.
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.
Make the caramel disk from sugar poured onto silicon paper or a silpat mat and cut with a round cutter while still warm before it sets
one option which may not be what you want but will provide consistent results is to make a nougatine. If you search for videos there is a technique where you make a praline then let it cool, blend it into a dust and then make dust enough to make a flat sheet on silicone may. This is then stuck in the oven to spread and harden as a completely flat layer and on removing from the oven is pliable enough to cut cleanly with a round cutter - but when it cools it's crisp and brittle. I'm traveling at the moment with poor internet but im sure there are examples of making perfect discs with these techniques online.