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—or for that matter, chopped bar chocolate—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.

The only way that I know to get them to have a near-liquid center would be to either warm them back up, or to use something that's already liquid at room temperature.

I don't know if I would recommend this to someone without much baking experience, but for someone comfortable with baking and who wants to experiment ... I'd try the following. (note, this is pure conjecture, I've never done this myself) :

1. Make a fudge sauce that's liquid (or at least gooey) at room temperature
2. Chill it enough so that you can shape it, or find some molds of a decent size
3. Pipe it out onto a chilled sheet tray to make blobs of your intended size
4. Make your cookie dough, and chill it down.
5. Assemble the cookies and bake them.

... it's quite possible that they won't keep for very long without chilling them (so you'd have to let them sit out to get back to liquid again, or warm them up through some other means).

Also possibly of interest -- I've found that letting a container of chocolate chip cookies sit in a closed car for an hour or two brings them back to that just-slightly-melted quality that you get from fresh baked cookies.

A ganache filling would work well. Ganache is simply a mixture of heavy cream and chopped chocolate. I think a 1:1 ratio would work, meaning equal amounts (by weight) of chocolate and cream.

Chop some chocolate into small pieces and put in a large bowl. (You can also use chocolate chips if you'd rather.) Heat the heavy cream until it is steaming but not boiling. Pour over the chocolate and let it sit for a minute or so. Then stir until the chocolate and cream are completely mixed. This will take several minutes. Chill in the refrigerator.

Scoop out your cookie dough as you normally would. Take a piece of the cookie dough and wrap it around a small scoop of the ganache. Roll it around in your hand to even it out and make sure the ganache is completely covered. Repeat with the rest of the cookie dough. Then bake the cookies.

The ganache will stay soft even after the cookies have cooled. The filling won't be liquidy (like "lava") but soft and fudgy. You can experiment with different ratios of cream and chocolate to make the ganache thicker or thinner.

Make chocolate sauce with FOS (Fructooligosaccharide) liquid. FOS does not recrystallize like sugar. I thus helps to maintain the chocolate smooth and in liquid state at room temperature. Gently melt together '2 tbsn Butter+ 4 Tbsn FOS+ 6 Tbsn cocoa powder'. (Add more FOS for sweetness, if required). Its liquid at room temperature. Freeze and then add to cookies, while rolling out. The chocolate is in a molten state even at room temperature.