Preheat your oven to 350°F (175°C). Line two baking sheets with parchment paper or silicone baking mats. Set aside.

In a medium bowl, whisk together the all-purpose flour, cocoa powder, baking soda, and salt. Set aside.

In a large mixing bowl, combine the melted and slightly cooled butter with the granulated sugar and packed light brown sugar. Beat with an electric mixer on medium speed until creamy and well combined, about 1-2 minutes.

Beat in the room temperature large egg and vanilla extract until just combined and smooth. Do not overmix.

Gradually add the dry ingredient mixture to the wet ingredients, mixing on low speed until just combined. Be careful not to overmix; a few streaks of flour are fine.

Fold in the semi-sweet chocolate chips and milk chocolate chips using a rubber spatula until evenly distributed throughout the dough.

Cover the bowl with plastic wrap and chill the dough in the refrigerator for at least 30 minutes. This helps prevent the cookies from spreading too much and enhances flavor.

Drop rounded tablespoons of cookie dough (or use a 1.5-inch cookie scoop) onto the 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. Do not overbake for chewy cookies.

Remove from the oven and let the cookies cool on the baking sheets for 5 minutes before transferring them to a wire rack to cool completely. This prevents them from breaking apart.