Preheat oven to 350 degrees F. Line baking sheet with parchment paper. Set aside.
In a medium size mixing bowl, whisk together the flour, baking soda, cornstarch, and salt. Set aside.
In a medium sauce pan, combine the butter and the cocoa powder over medium heat. Stir until the butter is melted and the cocoa powder is incorporated. It should look shiny and smooth. Allow to cool to room temperature.
In the bowl of an electric mixer, fitted with the paddle attachment, combine the butter mixture with the brown sugar and granulated sugar. Mix on medium speed until the texture is smooth, about two minutes.
Stir in the eggs and the vanilla extract until combined.
With the mixer on low, stir in the flour mixture until no streaks of flour remain. Stir in the milk chocolate chips.
Refrigerate the dough for an hour to allow the consistency to firm up a bit. This will make it easier to work with when you add the white chocolate.
Using a 1-inch cookie scoop, scoop out 52 balls of dough and place on a piece of parchment paper. Two of those balls of dough will create ONE cookie.
Slightly flatten one ball of dough, place the white chocolate piece in the center and then top with another ball of cookie dough. Use your fingers to connect and seal the sides of the cookie. You should have enough for 26 cookies total.
Place the cookies on the baking sheet with plenty of room between each. These cookies will spread quite a bit. I did 8 cookies on my cookie sheet: three on the sides and two in the center row.
Bake for about 10 minutes.
Allow to cool for about 5 minutes and then enjoy WARM!