Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9-inch square baking pan and line with parchment paper, leaving the paper hanging over on 2 opposite sides.

Place semisweet chocolate and butter into a microwave-safe bowl. Melt chocolate in a microwave in 15-second intervals, stirring after each interval, 1 to 3 minutes.

Beat brown sugar, eggs, and orange zest together using an electric mixer in a bowl until thick and fluffy. Fold in chocolate mixture.

Sift flour and cocoa together into a separate bowl; stir in chocolate mixture. Stir in white chocolate bits. Spread into the prepared baking pan.

Bake in the preheated oven until a toothpick inserted into the center comes out mostly clean, about 40 minutes. Let cool in the pan completely before lifting out, 15 to 30 minutes, using the paper as handles. Cut into squares.