Place an oven rack in position C and preheat the oven to 350°F. Prepare an 8-inch aluminum baking pan (see pages 180-183).
Sift together the dry ingredients in the food processor.
In an electric stand mixer fitted with a whisk attachment, whip the eggs at medium speed until light (both in texture and color). Add the vanilla.
Mix the sugars together, reduce the mixer speed to 30-percent power, and add the sugars to the eggs, incorporating thoroughly.
Add the butter and remaining dry ingredients in three alternating doses, starting with the wet and finishing with the dry. Fold in the nuts.
Pour the batter into the prepared pan and bake for 55 to 60 minutes. Check for doneness with the tried-and-true toothpick method: a toothpick inserted into the center of the pan should come out clean.
Remove the pan to a cooling rack and resist the temptation to cut until the brownies are completely cool. When ready, cut into squares with a pizza cutter.