Great idea for using corks. I have made several cork-topped trivets in the past, and would also like to know if you split them and also, what type of adhesive you used to attach them to the backing?
I use Titebond 3 to attach my corks to the plywood brivet top, and I do split them. I use my bandsaw for that: very quick and easier than cutting them with a knife.
Nice work. I blame my friends for my cork collection.
Steve