3 oz. (2/3 cup) unbleached all-purpose flour; more for the pan
2 cups granulated sugar
4 large eggs, at room temperature
1/2 tsp. pure vanilla extract
2-1/2 oz. (3/4 cup) unsweetened natural cocoa powder
1/2 tsp. baking powder
1/2 tsp. table salt
Preheat oven to 350 degrees. Line a 8 or 9 inch square pan with tinfoil.
Melt the butter in a medium saucepan over medium heat. Remove the pan from the heat. Whisk or stir in the sugar, followed by all four of the eggs and the vanilla. Stir in the flour, cocoa, baking powder, and salt, starting slowly to keep the ingredients from flying out of the pan and stirring more vigorously as you go. Stir until the batter is smooth and uniform, about 1 minute.
Spread the batter into the prepared baking pan, smoothing it so it fills the pan evenly. Bake until a toothpick or a skewer inserted 3/4 inch into the center of the brownies comes out with just a few moist clumps clinging to it, about 40 minutes
