Preheat the oven to 350°F (180°C).
Line an 8-inch square pan with 2 long lengths of aluminum foil or parchment paper, positioning the sheets perpendicular to one other and allowing the excess to extend beyond the edges of the pan. Lightly butter the foil or parchment.
In a medium saucepan over low heat, melt the butter. Add the chocolate and whisk until it's completely melted and smooth.
Remove the pan from the heat and, still using the whisk, stir in the sugar and vanilla until combined.
Whisk in the eggs by hand, 1 at a time. Add the flour and whisk with everything you've got until the batter loses its graininess, becomes smooth and glossy, and pulls away a bit from the sides of the saucepan, 1 to 1 1/2 minutes. Seriously, time yourself. During stirring, the batter may appear to separate, and midway through stirring it may appear grainy, but when you keep whisking with vigor, you'll end up with a batter that's rich and thick.
Stir in the chopped nuts and scrape the batter into the prepared pan. Bake until the center is almost set, 25 to 30 minutes. Do not overbake.
Place the pan on a wire rack and let the brownies cool completely—yes, we understand how difficult this can be—before removing them from the pan by lifting the foil or parchment paper. Cut into 9 squares. (In theory, the brownies will keep, covered, at room temperature for up to 4 days and in the freezer for up to 1 month. But c'mon. We both know that's not going to happen.)