Begin with baking the cakes, the filling and frosting will come later.
Preheat the oven to 350º. Line two cupcake pans with paper liners (24 total).
In the bowl of a stand mixer fitted with the paddle attachment, combine the butter and brown sugar. Beat together on medium-high speed until light and fluffy, about 3 minutes. Mix the eggs in one at a time, beating well after each addition and scraping down the sides of the bowl as needed.
Combine the flour, baking powder, baking soda, and salt in a medium bowl. Stir together to blend. Add the dry ingredients to the mixer bowl on low speed, alternating with the milk, beginning and ending with the dry ingredients. Mix each addition until just incorporated. Blend in the vanilla. Fold in the chocolate chips with a spatula.
Divide the batter evenly between the prepared cupcake liners. Bake for 18-20 minutes, until a toothpick inserted in the center comes out clean. Allow to cool in the pan 5-10 minutes, then transfer to a wire rack to cool completely.
While the cupcakes are cooling, make the filling.
Combine the butter and sugar in a mixing bowl and cream on medium-high speed until light and fluffy, about 2 minutes. Beat in the flour, sweetened condensed milk, and vanilla until incorporated and smooth. Stir in the chocolate chips. Cover with plastic wrap and refrigerate until the mixture has firmed up a bit, about an hour.
In the meantime, make the frosting for the cupcakes.
Beat together the butter and brown sugar in the bowl of a stand mixer fitting with a paddle attachment until creamy. Mix in the confectioners' sugar until smooth. Beat in the flour and salt. Mix in the milk and vanilla extract until smooth and well blended.
After about an hour, and the mixture has firmed up, cut a cone-shaped portion out of the center of each cupcake (I used a paring knife). Fill each hole with a chunk of the chilled cookie dough mixture.
When the filling has been inserted into the cupcake, you may frost the cupcakes as desired. I sprinkled mine with mini chocolate chips, but you may also add some mini chocolate chip cookies for decoration.