Preheat the oven to 350°F. Line an 8-inch square baking pan with parchment paper, leaving an overhang on the sides to lift the brownies out easily.

Combine the butter and chopped milk chocolate in a microwave-safe bowl. Heat in 30-second intervals, stirring between each, until melted and smooth.

Stir granulated sugar and brown sugar into the melted chocolate mixture. Add eggs, one at a time, mixing well after each addition. Stir in vanilla extract.

Sift together flour, cocoa powder, and salt. Gradually fold the dry ingredients into the chocolate mixture using a spatula, just until combined.

Fold in 1/2 cup of the milk chocolate chips. Spread the batter evenly into the prepared pan. Sprinkle the remaining 1/4 cup chocolate chips on top.

Bake in the preheated oven for 22-25 minutes, or until a toothpick inserted in the center comes out with a few moist crumbs. Avoid overbaking to ensure fudginess.

Allow the brownies to cool in the pan on a wire rack before lifting out using the parchment overhang. Cut into squares and serve.