It appears to be a bit of a right of passage for a baking blog to feature a cookie dough cupcake recipe. I've staked a number of them on pinterest, (like this one and this one and this one), and they came in two varieties-- the kind that stuff with dough post-baking and the kind that freeze the dough and bake it inside. I opted to go the route of freezing the dough, so that it really goes in the middle and so that you can get a little in every bite. Consequently, I also went about deciding how to make my favorite cookie dough egg-less, as the dough stays doughy and I have no desire to send anyone into the grips of Salmonella, or any other brand of food poisoning. This post by The Girl Who Ate Everything gave me the idea to substitute the egg with sweetened condensed milk, which worked perfectly. I combined my newly egg-less dough with my favorite vanilla cupcake recipe, doctored up a little vanilla butter-cream to hold a more cookie-like flavor, and DONE. They are delicious.
You'll notice that this vanilla cupcake recipe is the same one I've used as a base for a lot of recipes. I like it because it is consistent and easy. I have a few other recipes I'll bust out for you at another time, but I specifically chose this one for these cupcakes because the batter is thick. It's the same one I use as the base for my cupcakes with Oreos baked inside. You need a thick batter when you want something to bake in the middle-- this helps prevent the stuff in the middle from sinking to the bottom.

