Melted chocolate inside the cookies
Assuming the cookie you mean is basically a filled chocolate chip cookie baked in a muffin tin with a chocolate filling:

With one exception all of the top recipes call for chocolate chips as the filling (the exception using a commercial fudge product).  Some used regular, one used milk chocolate chips.  Given the way the recipe works, any chocolate chip&mdash;or for that matter, chopped bar chocolate&mdash;will work, although you will want to select quality brand that is actually true chocolate if you can.

You cannot keep chocolate from re-hardening when it cools.  This recipe is meant to be eaten warm from the oven, when the chips are still melted. 

If you have used a brand of chip that is true chocolate (with cocoa butter, not a replacement fat), you may have some success reheating them in the microwave, to remelt the chocolate.  The fat in the chocolate chips will absorb microwaves better than the surrounding cookie dough, so the chocolate should melt relatively quickly.   This may or may not work with chips where the cocoa butter has been replaced with other fats.