How to bake soft cookies with hard chocolate chunks?

Baking soft cookies is no problem, but the chips/chunks stay molten even after the cookies cool, which I personally think is gross. I want the chocolate to harden once the cookies cool to room temperature. I used to be able to do this with a particular brand of plain semi-sweet baking chocolate, but it's no longer available to me. I tried a Hershey's Special bar, but the chunks from that melted again at room temp even after the cookies spent some time in the fridge. Is it just a matter of finding the right chocolate, or does the recipe affect that somehow, too?