Start by bringing your butter to room temperature so it’s soft enough to cream without melting. Preheat your oven to 350°F (175°C) and line baking sheets with parchment paper.
In your mixer bowl, beat the butter, sugar, and brown sugar together on medium speed until the mixture is light, fluffy, and creamy – about 3 to 5 minutes.
Beat in the eggs one at a time, ensuring each is fully incorporated before adding the next. Then mix in the vanilla extract. The dough will start to look glossy and smooth.
In a separate bowl, sift together the flour, cocoa powder, baking soda, and salt to ensure even distribution and prevent clumps.
Gradually add the dry ingredients to the wet mixture, mixing on low speed until just combined. Be careful not to overmix.
Using a spatula, gently fold in the milk chocolate chips and white chocolate chips until evenly distributed throughout the dough.
Use a cookie scoop or tablespoon to drop dough balls onto your prepared baking sheets, spacing them about 2 inches apart. Bake for 10-12 minutes, or until the edges are set but the centers still look slightly soft.
Allow the cookies to cool on the baking sheet for 5 minutes before transferring them to a wire rack to cool completely.