Prep the pans, oven, and eggs. Arrange a rack in the middle of your oven and preheat to 350°F/180°C. Prepare a pan by lining it either with foil or parchment paper and lightly grease.

Place your eggs in a bowl of the hottest tap water, switching out a couple of times until the eggs feel slightly warm to the touch.

Brown the butter/make cocoa powder paste. First, add the cocoa powder and salt to a heatproof bowl and set that aside.

Next, add the butter to a light-colored pan and melt on medium heat. The butter will first melt, and a cream-colored foam will rise. If the butter sputters and pops, turn the heat down a little lower so it doesn’t make a mess. Take a wooden or silicone spatula and start stirring. The milk solids usually form around the edge and bottom of the pan first. This may take a couple of minutes. Scrape the pan so milk solids don’t stick and burn. Turn off the heat once the solids are a light brown and continue stirring until they reach a dark brown. Immediately pour the melted butter into the cocoa powder bowl, being sure to scrape those milk solids. Stir the mixture and set aside until slightly warm to the touch, about 5-10 minutes.

Mix the eggs with powdered sugar. Meanwhile, add the room-temperature eggs and yolks with powdered sugar to a large mixing bowl. Use a hand whisk or spatula and mix the eggs and sugar until you can no longer see traces of sugar. If the powdered sugar is clumpy, smash it with the spatula and allow it to sit for 5-10 minutes while your chocolate mixture cools. The final mixture will be pale yellow and slightly thickened. The mixture should feel like a smooth paste if you feel the mixture with your fingers.

Add the rest of the ingredients to the egg mixture. At this point, the cocoa powder butter mixture should be slightly warm. Stir the vanilla extract into the mixture and then add that to the eggs. Use a spatula to mix until nice and thick. Ensure the brown sugar has no clumps, and fold that into your batter with a spatula. Fold in the flour. The batter will be very thick.

Pour batter into pan and add chocolate pieces. I like to preserve the crackly sugar top on my brownies, so I set aside about a fourth of the batter. Then, I mix the chocolate pieces into the remaining larger quantity of batter and pour that into the pan. I then pour the batter I set aside on top on, smooth it out.

Bake for about 20-25 minutes. Place the brownie pan on the middle rack. For the 8x8 pan, start checking at 18 minutes. For the 9x13 pan, start checking around 20 minutes. The final brownies should have puffed up with a glossy crystallized sugar top. They will be slightly jiggly in the center, and a toothpick inserted in the middle will come out with streaks of wet batter.

Cool brownies completely in the pan. Then, pull the parchment or foil sling out and slice them into squares to serve.