Whip eggs using a stand mixer with the whisk attachment on medium speed until lightened and increased in volume. (They will be foamy.) Add vanilla.
With the mixer on medium-low speed, add the sugar and brown sugar. Mix until combined.
In a separate bowl, whisk together the cocoa, flour, and salt. (I often skip this step of sifting together dry ingredients in other recipes, and likely will skip it here in the future too.)
With the mixer on low, alternate adding the melted butter and the cocoa mixture in 3 additions, beginning with the butter and ending with the cocoa. Mix until just combined, and be sure to scrape down the sides of the bowl.
Pour batter into a parchment-lined (or greased) metal 8x8-inch pan.
Bake at 350F for 45-60 minutes (originally 55-60, but mine were done at 50 minutes). A toothpick inserted in the center of the brownies will come out with gooey crumbs stuck to it.
Cool for at least an hour before removing from the pan. Store in an airtight container at room temperature.
Notes
A metal 8x8-inch pan is a must for this recipe, as it bakes a long time. Do not use a flour baking spray on it. Parchment is nice for easy removal.I've included weights for the dry ingredients; they come from the cookbook. I weighed those ingredients.If your toothpick comes out of the brownies clean, your brownies are overbaked. In that case, add some chocolate chips to the top while brownies are hot (so they get melty), or add frosting.Need a frosting? Here's the one Alton Brown suggests: 6.5 ounces (1 cup) semisweet chocolate, ½ cup cream, and 1 cup butter melted together, with 2 ½ cups powdered sugar mixed in with a hand mixer. Adapted from Alton Brown's I'm Just Here for More Food