Preheat oven to 350°. Line a 9-inch square baking pan with aluminum foil, letting the excess hang over the edges. Lightly butter the foil.
Melt butter and chocolate on low heat on the stovetop in a saucepan or in the microwave in a microwave-safe bowl. Remove from heat or microwave. One at a time, whisk in cocoa, sugar, eggs, vanilla, and flour. Pour into prepared pan. Smooth the top of the batter. Sprinkle salt over top of batter. Using a butter knife, swirl salt into brownie batter.
Bake for 30-35 minutes, until edges are set and center is a bit soft. A toothpick inserted in the center should come out with a little batter coating it.
Cool at room temperature for an hour. Then, cool in refrigerator for an hour or until firm. Remove from pan and foil. Serve at room temperature.
Brownies can be refrigerated for 3 days or frozen for a month.