Preheat & Prep: Position an oven rack in the middle of the oven and heat to 325°F (162°C). Line an 8-inch square baking pan with parchment paper or aluminum foil, leaving an overhang on opposite sides.
Melt Butter: Add butter to a medium saucepan. Place over medium-low heat and cook until butter melts completely, then turn off the heat. Do not let it brown.
Combine Hot Ingredients: While the butter is hot, stir in the sugar, cocoa powder, vanilla, and salt. Stir well until blended. The batter will look gritty.
Cool Slightly: Set the saucepan aside to cool until the mixture is warm, not hot, about 5 to 10 minutes.
Add Eggs: Add the cold eggs, one at a time, stirring vigorously with a whisk or spoon after each egg until the batter looks thick, smooth, and well blended.
Add Flour: Add the flour. Use a wooden spoon or spatula and beat the flour into the batter for 40 to 50 strokes, or until it is very thick and pulls away from the sides of the saucepan.
Stir in Optional Add-ins: Gently stir in nuts or chocolate chips if using.
Spread & Bake: Spread the thick brownie batter evenly in the prepared pan. Bake for 20 to 30 minutes, or until the edges look dry and the middle is slightly underbaked. A toothpick inserted into the center should emerge with moist crumbs or a little wet batter.
Cool Completely: This is essential. Let the brownies cool completely in the pan on a wire rack before lifting out using the parchment overhang and slicing into 16 squares. This helps them set to the perfect fudgy consistency.
