I didn't have any normal size carrots so I had to make due with these mini carrot things. (I'm guessing you could use a potato as well). First I cut a piece 1/4" thick. Then I used the same cutter that I was trying to make the cookies with and cut out a carrot heart. I shaved off some of the edges (using the same cutter) so it would easily pass back and forth through the cutter. Then I carefully pushed the toothpick into it.
I've wrapped the whole thing with a piece of plastic baggie and a twist tie. Not the prettiest looking thing, but it didn't have to be because I was going to throw it away once I was finished.
Here it is actually pushing out a mini heart.
All done! Only a hundred more to go.