Are there ice cube trays that make thin or partially frozen ice cubes?

Ice cubes seem so much more refreshing when they haven’t frozen through all of the way. I love to take them out of the freezer and eat them when the centers are still water. Can you buy an ice cube tray that leaves the centers empty or unfrozen and what would something like that be called? Maybe just a tray that makes really thin ice-sheets instead of cubes?

Yes, I know this is a weird question.