Combine butter and both sugars in a mixing bowl and cream on medium-high speed until light and fluffy, about 2 minutes. Beat in milk and vanilla until incorporated and smooth. Beat in the flour and salt until just combined. Stir in chocolate chips. Scoop about 1.5 tablespoons of dough at a time, and shape into balls. Place cookie dough balls on a parchment or foil-lined baking sheet. Cover with plastic wrap and freeze overnight. I froze mine for 24 hours.
For The Cupcakes
Preheat oven to 350 degrees. 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 in the eggs, 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 just until incorporated. Blend in the vanilla.
Fill the cupcake liners about 2/3 full with the cupcake batter. Place a frozen cookie dough ball on the top center of each cupcake. Bake at 350 for 16-18 minutes.
Be sure to only fill cupcake liners 2/3 of the way full with the batter. You don't want the cupcakes overflowing while they bake. You may have a little bit of batter left over after filling all 24 cupcake liners.
For The Classic Vanilla Buttercream Frosting
Place butter in a large mixing bowl. Beat on medium speed until creamy. Slowly add in the powdered sugar one cup at a time, beating on medium speed until smooth. Pour in half & half, salt, and vanilla, and continue to beat until smooth and combined.
Frost cooled cupcakes and sprinkle with mini chocolate chips. Enjoy!