Preheat the oven to 350°F / 180°C (160° fan-assisted) and line a square pan with parchment paper.
Chop the chocolate into small pieces and put it into a heatproof bowl along with the butter. Melt them together either in a double boiler or in the microwave in 30-second bursts, stirring in between until completely melted. Set aside to cool while you proceed to the next step.
Combine the sugar and eggs in a large bowl and whisk until pale and thick. This should take about 60 seconds of vigorous whisking by hand. You can use an electric mixer if you prefer, but it's not necessary.
Pour the cooled melted chocolate mixture into the egg/sugar mixture, add the vanilla, and gently whisk everything together until fully incorporated.
Sift the flour and salt into the bowl and use a spoon or spatula to fold everything together until there are no more visible lumps of flour.
Pour the brownie batter into the prepared pan and spread it out into an even layer.
Bake for 25-30 minutes until the brownies are set and the tops are dry and shiny.
Let the brownies cool in the pan completely before attempting to remove them, they will continue to bake as they cool.
Notes
Use real chocolate, not chocolate chips or chocolate candy bars, as these have additives in them to prevent them from melting properly. Do not try to unmold the brownies before they have completely cooled - they will still be extremely soft and gooey on the inside. You cannot test if the brownies are done using the typical toothpick test, as these are super fudgy brownies. See the post above for tips on how to know when they are baked.