• Preheat the oven to 350 degrees F. Position the oven racks in the lower-middle and upper-middle positions. Use parchment paper or silicone baking mats to line two baking sheets.
• Mix flour, baking powder, and baking soda together in a large bowl.
• To loosen the butter, beat it for 30 seconds at medium speed. Mix for about three minutes on medium-high speed while gradually adding the sugar, cocoa powder, and vanilla.
• Scrape down the sides of the bowl and add the eggs and vanilla. Beat at medium speed until combined, about 30 seconds.
• Repeat the scraping process on the sides and bottom of the bowl. As you add the flour to the mixer on low speed, alternate adding the milk in three additions and mixing until just combined.
• Ensure the flour has been incorporated by giving the mixture a few final stirs with a rubber spatula.
• To portion out the dough mounds, use a #20 scoop and place them about two inches apart on the prepared baking sheets.
• Make three-inch circles with each mound of dough using an offset spatula.
• On a baking sheet, bake the cookies for about 12 minutes, or until the edges are golden brown.
• Cool the cookies completely on a wire rack after cooling them on the baking sheets for two minutes.

Vanilla Frosting

• Using a small bowl, cream the butter. With the milk alternately, blend in the confectioner's sugar, vanilla, and 1/3 cup of confectioner's sugar. Make sure there are no lumps in the mixture and beat until it is creamy.
• Take just over half of the frosting and place it in a separate bowl, leaving the remainder to be whipped into fudge frosting.

To Make the Fudge Frosting

• Add 1-2 tablespoons of additional milk to the mixing bowl along with 1/3 cup cocoa powder.
• Using an electric mixer, beat the frosting until it is smooth and the cocoa has been incorporated.
• Use white frosting to frost the top of the cookies, about half of the cookies be covered with white frosting. Chocolate should be frosted on half of the cookie.