Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats for easy cleanup and even baking.
In a large mixing bowl, combine the softened butter, brown sugar, and granulated sugar. Use an electric mixer or stand mixer to cream them together until light and fluffy, about 2-3 minutes.
Add in the eggs, one at a time, mixing well after each addition. Then, add the vanilla extract and mix until everything is fully incorporated.
Sift the cocoa powder, flour, baking soda, and salt into the wet ingredients. Gradually mix until just combined, being careful not to overmix the dough.
Gently fold in the semi-sweet and milk chocolate chips with a spatula, distributing them evenly throughout the dough.
Use a cookie scoop or tablespoon to portion out the dough onto the prepared baking sheets, spacing each cookie about 2 inches apart to allow for spreading.
Bake for 11 minutes, or until the edges are set but the centers still look slightly soft.
Remove the cookies from the oven and allow them to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.