Heat the oven to 350°F (175°C). Lightly grease an 8-inch square metal pan and line it with parchment, leaving an overhang on two sides.

Melt the butter and chopped bittersweet chocolate in a medium saucepan over low heat, stirring often. Remove from the heat while a few soft chocolate pieces remain, then stir until completely smooth.

Whisk the granulated and brown sugars into the warm chocolate mixture. Let cool for 5 minutes so the eggs will not scramble.

Whisk in the eggs and extra yolk one at a time, then whisk in the vanilla for about 1 minute until the batter looks thick and glossy.

Sift the flour, cocoa powder, and salt over the batter. Fold gently just until no dry streaks remain. Fold in the chocolate chips, if using, then spread the batter evenly in the prepared pan.

Bake for 24 to 28 minutes, until the edges are set and a toothpick near the center comes out with moist crumbs but no liquid batter. Cool completely in the pan for at least 2 hours before lifting out and cutting into 16 squares.