These are the best brownies I have ever made, and I've made them hundreds of times. They have the kind of fudgy chocolatiness that wimpy people say is too chocolaty — silly little rabbits.
Preheat the oven to 350 F. Generously butter a 13-by-9-inch baking pan or spray it with nonstick cooking spray.
Place the butter and chocolate in a medium-sized saucepan over low heat and let melt together, stirring until smooth. Remove the saucepan from the heat and stir in the cocoa powder, sugar, and salt, then blend in the vanilla. Beat in the eggs one at a time, stirring to mix quickly so they don’t have a chance to cook at all before they are blended in. Blend in the flour.
Scrape the thick batter into the prepared baking pan and smooth the top with a spatula. Bake until the edges just begin to pull away from the sides of the pan and a wooden skewer or toothpick inserted into the middle comes out clean, 25 to 30 minutes.
Let the brownies cool in the pan on a wire rack. When completely cool, cut them into 12 or 24 squares.
Notes
Often, a recipe will tell you to chop the chocolate before melting it. Here, you just make sure to melt it with the butter over low heat, and the chocolate will dissolve gently into the butter without scorching.
Also, you can skip the whole double boiler thing if you keep the heat low enough, don’t stray too far, and stir frequently. This saves you washing a chopping board, a knife (or a food processor bowl and blade), and the second double boiler pan. You will want to celebrate this with a brownie.
The batter is very thick and will need to be spread out evenly in the pan. It will thicken even further as it cools, so it's best to get it into the pan as soon as it's blended.
Another reminder to let the brownies cool completely before slicing, as the fudginess will cause them to fall apart if warm.
Storage
The brownies can be made ahead and kept in a sealed container or well-wrapped at room temperature for up to 5 days.
The brownies can be frozen for up to 6 months. Wrap them in foil or plastic wrap, then tuck them into a labeled freezer-proof bag. Press out all the excess air, seal, and freeze.