4 ounces (1/2 cup or 8 tablespoons) unsalted butter; more for pan
4 ounces unsweetened chocolate
1-1/2 cups granulated sugar
Scant 1/4 teaspoon salt
2 teaspoons pure vanilla extract
2 large eggs, at room temperature
4-1/2 ounces (1 cup) all-purpose flour
2 tablespoons unsweetened natural cocoa powder (not Dutch-processed)
Position a rack in the middle of the oven; heat the oven to 350 degrees F. Butter an 8-inch square pan, line the pan bottom with parchment, and then butter the parchment.
Melt the butter and chocolate together in a medium metal bowl, set over a pan of simmering water. Let the chocolate cool slightly before stirring in the sugar, salt and vanilla.
Add the eggs one at a time, stirring each time until blended. Add the flour and cocoa and beat until the mixture is smooth, 30 to 60 seconds. Scrape the batter into the prepared pan and bake until the top is uniformly colored with no indentation and a toothpick inserted in the middle comes out almost clean, with a few moist crumbs clinging to it, 35 to 45 minutes.
Set the pan on a rack until cool enough to handle. Run a paring knife around the inside edge of the pan, and then invert the pan onto a flat surface and peel off the parchment. Flip the baked brownie back onto the rack to cool completely. Cut into squares.