Preheat the oven to 350°F (175°C). Grease an 8-inch cake pan. Line the pan with parchment and grease the top of the parchment (or line with non-stick foil). Set the pan aside.

Before melting chocolate, set aside 1 ounce of the chopped unsweetened chocolate and 2 tablespoons of the butter for the ganache topping. Use the remaining chocolate and butter for the batter.

In a medium bowl, beat the 2 eggs and ½ teaspoon salt with a hand-held electric mixer until frothy.

Add the 1 cup sugar to the eggs and beat 2 to 3 minutes, until the mixture is thick and pale yellow. Add the 1 tablespoon vanilla and beat just to combine.

In a microwave-safe bowl, microwave the reserved-for-batter butter and chocolate mixture (the butter and chocolate you did not set aside) for about 1 minute on high. Stir, then continue to microwave in 15–30 second increments, stirring between each, until the chocolate is fully melted and the mixture is smooth.

With the mixer running on low, slowly pour the melted chocolate-butter mixture into the egg mixture. Scrape down the bowl as needed.

Add the ½ cup flour and beat just until incorporated, less than a minute. Scrape the batter into the prepared pan and smooth the top.

Bake for 20 minutes, or until the center is just barely set (a toothpick inserted near the center should come out with a few moist crumbs). Remove the pan from the oven and transfer to a wire rack to cool while you make the topping.

For the ganache-style topping: place the reserved 1 ounce chopped chocolate and the 2 tablespoons reserved butter in a microwave-safe bowl. Microwave about 30–45 seconds, then stir. Continue in short increments, stirring each time, until the chocolate and butter are melted and smooth.

Pour the melted chocolate-butter mixture over the cooled brownies and spread evenly. Chill the brownies in the refrigerator until the topping is set.

For easier cutting, place the chilled brownies in the freezer for at least 30 minutes before slicing. Allow individual slices to come to room temperature briefly before serving.