Preheat oven to 400 degrees F (200 degrees C). Lightly grease an 8-inch square baking dish.
Combine sugar, butter, and vanilla extract in a large bowl; beat with an electric mixer until smooth and creamy. Add eggs one at a time, beating well after each addition.
Combine cornstarch, cocoa powder, and salt in a bowl and sift over the sugar-butter mixture. Beat in slowly with a wooden spoon or spatula until all ingredients are well incorporated. Fold in chopped chocolate and let batter rest for 5 minutes. Pour brownie batter into the prepared baking dish.
Bake in the preheated oven until a toothpick inserted into the middle comes out clean, about 20 minutes. Remove from oven. Let cool completely before cutting into squares, about 15 minutes.