In a large mixing bowl, combine the softened butter, granulated sugar, and brown sugar. Using a stand mixer fitted with the paddle attachment or a hand mixer, beat on medium speed until the mixture is light and fluffy, about 2 minutes.

Add the egg and continue mixing until fully incorporated and smooth.

Add the flour, cocoa powder, baking soda, and baking powder. Mix on low speed just until the dough comes together. Avoid overmixing.

Fold in the chopped dark and milk chocolate using a spatula or mix briefly on low speed. Stop mixing as soon as the chocolate is evenly distributed throughout the dough.

Use an ice cream scoop to portion the dough into even balls, about 80 grams each. Place them on a parchment-lined tray and transfer to the freezer for 25 minutes.

While the dough chills, preheat the oven to 355°F (180°C) with the convection (turbo) setting.

Arrange 6 dough balls on a parchment-lined baking sheet, spacing them generously to allow for spreading. Bake for 13 minutes, until the edges are set and the centers are still soft.

Remove from the oven and let the cookies cool completely on the baking sheet. They will continue to set as they cool.