To Make the cookie dough filling: In a medium bowl, beat together butter, granulated sugar, and brown sugar until light and fluffy. Beat in the milk and vanilla until smooth. Mix in the flour and salt just until dough comes together and no streaks of flour remain. Fold in the chocolate chips. Line a baking sheet with parchment. Break off a golf ball size piece of dough and roll into a ball. Place on prepared baking sheet and repeat with remaining pieces.
To make the cookies: Set the oven racks in the upper and lower thirds of the oven. Preheat to 325 degrees F and line 2 baking sheets with parchment or lightly grease.
In a medium bowl, whisk together flour, baking soda, and salt.
In a large bowl, beat together butter, light brown sugar, and granulated sugar. Beat in the egg, egg yolk, and vanilla extract. Stir in the flour mixture until just combined and dough forms. Fold in the chocolate chips.
Roll a teaspoon size piece of dough into a ball, then break into two equal pieces. Place on the prepared baking sheets 1 inch apart, with torn edges facing up. Repeat with remaining dough.
Bake in preheated oven for 4 minutes. Turn and rotate the baking sheets, then continue to bake until lightly golden, another 3-4 minutes. Allow to cool on baking sheets before storing in an airtight container.
To make the cupcakes: Preheat oven to 350 degrees F and line 24 muffin tins with cupcake liners.
In a large bowl, beat together butter and brown sugar until light and fluffy. Beat in the eggs, one at a time, then vanilla extract.
In a medium bowl, whisk together flour, baking powder, baking soda, and salt. Alternate adding in the flour mixture and milk to the beaten butter: 1/3rd of the flour, 1/2 the milk, 1/3 flour, 1/2 milk, then last 1/3 flour. Fold in the chocolate chips.
Fill the prepared cupcake liners halfway. Place one frozen cookie dough ball in the center of each batter filled liner, but do not press down. Bake in preheated oven until the edges become golden, 20-22 minutes. Cool in pan for 5-10 minutes before removing to a wire rack. Allow to cool completely before adding frosting.
To make the frosting: In a medium bowl, beat together butter and brown sugar until light and fluffy. Beat in the powdered sugar, then the salt, milk, and vanilla extract until smooth. Pipe or spread over the cooled cupcakes. Top with extra mini chocolate chips and the mini chocolate chip cookies.