Preheat oven to 350°F. Grease and flour a 9-inch square pan.
In a small saucepan over low heat, melt the butter and bittersweet chocolate chips together, stirring frequently until smooth. Remove from heat and set aside to cool until just lukewarm.
In a bowl, whisk the sugar, eggs, and vanilla extract together until well combined and slightly thickened.
Pour the cooled chocolate mixture into the egg mixture and stir until evenly blended.
Sift the unbleached all-purpose flour and the pinch of salt directly over the chocolate-egg mixture. Gently fold the dry ingredients in just until no dry streaks remain.
Spread the batter evenly into the prepared 9-inch pan.
Bake for 33 minutes, or until a toothpick inserted in the center comes out clean or with only crumbs (no wet batter).
Allow the brownies to cool in the pan for 1 hour. Cut into 16 squares.