Preheat oven to 350°F (175°C). Line an 8-inch square baking pan with parchment paper so that the paper overhangs by a few inches on two opposite sides. Lightly grease the lining and any exposed parts of the inside of the pan.
Place the chocolate and butter in a microwave-safe bowl. Heat in the microwave at half power in 30-second increments until the butter is melted and the chocolate melts when stirred. Stir until smooth. Set aside to cool slightly.
Place the sugar, brown sugar, eggs, and vanilla in a large mixing bowl, and mix until well-blended. Add the chocolate-butter mixture, and mix until smooth.
Add the flour and salt, and mix just until combined.
Transfer the batter to the prepared pan and spread evenly. Bake 35-40 minutes, or until a pick inserted into the center comes out with a few moist crumbs attached. Run a knife along the non-lined sides of the pan. Cool in the pan on a wire rack.
Using the overhanging parchment paper, lift the cooled brownies out of the pan and onto a cutting board. Use a sharp knife to cut into bars.
Notes
If you like nuts or more chocolate with your brownies, stir 1 cup of chopped nuts or chocolate chips into the mixed batter before transferring it to the pan.
Store in an airtight container at room temperature up to 4 days.