Preheat your oven to 350°F (175°C). Line an 8x8-inch baking pan with parchment paper.
Melt the chopped milk chocolate and butter together in a heatproof bowl over a double boiler or in the microwave. Stir until smooth.
Add white sugar and brown sugar to the melted chocolate mixture. Stir until combined.
Whisk in the eggs one at a time, mixing until fully incorporated.
Sift in the flour and cocoa powder, then gently fold until just combined. Do not overmix.
Fold in the milk chocolate chips for extra chocolatey goodness.
Pour the batter into the prepared baking pan and spread evenly.
Bake for 22-27 minutes, or until a toothpick inserted into the center comes out with a few moist crumbs.
Let the brownies cool in the pan for at least 3 hours before cutting into squares.