Preheat oven to 350 degrees F. Grease a 9x9-inch square baking pan, then line with parchment paper.
Bring the Guinness to a boil over medium-high heat in a small saucepan. Boil until reduced to ¼ cup, about 5 minutes. Set aside to cool.
Place the chocolate and butter in a heatproof bowl set over a saucepan of simmering water and stir occasionally until completely melted and smooth. Remove from the heat and set aside.
In a large bowl, whisk together the sugar, eggs and vanilla extract until thoroughly combined and pale yellow in color. Gradually whisk in the melted chocolate mixture, then the reduced Guinness. Add the flour and salt and fold into the batter with a rubber spatula until no streaks of flour remain.
Pour the batter into the prepared pan and bake until a toothpick comes out with moist crumbs attached, about 40 minutes. Remove from the oven and place the pan on a wire rack; cool completely before cutting and serving. The brownies should be stored in an airtight container at room temperature for up to 5 days.