Butter a 13 x 9-inch pan and line with buttered parchment paper (or lined with buttered foil).
Set rack at the middle level of the oven and preheat to 350°.
Bring a saucepan of water to a boil and turn off heat. Combine butter and chocolate in a heatproof bowl and set over pan of water. Stir occasionally until melted.
Whisk eggs together in a large bowl, then whisk in salt, sugars, and vanilla. Stir in chocolate and butter mixture, then fold in flour.
Pour batter into prepared pan and spread evenly. Bake for about 45 minutes, until top has formed a shiny crust and batter is moderately firm. Cool in pan on a rack. Wrap pan in plastic wrap and keep at room temperature or refrigerated until next day.
To cut brownies, unmold onto a cutting board, remove paper, and replace with another cutting board. Turn cake right side up and trim away edges. Cut brownies into 2-inch squares.
SERVING: Serve the brownies on their own or with ice cream and hot fudge sauce.
STORAGE: The best way to store brownies is to wrap them individually and keep them at room temperature in a tin or plastic container with a tight-fitting cover. Or freeze them.
NOTE: If you have a 12 x 18-inch commercial half-sheet pan, you may double this recipe easily.