Preheat oven to 350° and prepare 2 paper-lined muffin trays.
In a large bowl, sift together flour, salt, baking soda, and baking powder.
Using an electric mixer, in another bowl, cream butter and sugar on medium speed until light and fluffy, about 3 minutes.
Add eggs, one at a time, until well incorporated. Scrape down the sides of the bowl.
In alternating batches, add dry ingredients and milk, careful to avoid over-mixing. Add vanilla.
Remove cookie dough balls from the freezer. Fill each cup with batter about halfway. Insert 1 frozen cookie dough ball in the center of each cupcake and gently press down, allowing the batter to bake up over the dough.
Bake 16–18 minutes and allow to cool for several minutes in the pan before transferring cupcakes to a wire rack. Allow to cool completely before frosting.