Preheat your oven to 350°F (175°C). Grease a square 9x9-inch baking pan and set it aside.

In a 2-quart saucepan, melt the unsweetened chocolate and butter over low heat, stirring constantly until smooth. Remove the saucepan from the heat.

Stir in the granulated sugar, eggs, and vanilla extract into the chocolate mixture until well combined.

Add the all-purpose flour and salt to the mixture, and stir until just combined. Be careful not to overmix.

Pour the brownie batter into the prepared baking pan, spreading it evenly.

Bake the brownies in the preheated oven for 20-25 minutes, or until a toothpick inserted into the center comes out clean. The brownies should be set around the edges but slightly gooey in the center.

Once done, remove the pan from the oven and allow the brownies to cool completely before cutting them into squares.

Serve and enjoy the fudgy brownies!