Preheat the oven to 350°F. Line a baking sheet with parchment paper.
In a large mixing bowl, beat the softened butter, granulated sugar, and brown sugar together for 2 to 3 minutes, until light and fluffy.
Add the eggs, vanilla extract, and milk. Mix until smooth and fully combined.
In a separate bowl, whisk together the flour, Dutch-process cocoa powder, cornstarch, baking soda, baking powder, and salt.
Gradually add the dry ingredients to the wet ingredients and mix until a thick, soft dough forms. The dough will be soft and slightly sticky.
Chill the dough for 15 to 20 minutes.
Scoop the dough into 8 large portions, about ¼ cup each, and place them on the prepared baking sheet. Gently flatten each one into a thick disc.
Bake for 11 to 12 minutes, until the edges are set and the centers still look soft but no longer glossy or wet.
Let the cookies cool on the baking sheet for 10 minutes, then transfer to a wire rack to cool completely.