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Place a rack in middle of oven; preheat to 325°. Lightly coat a 9x9" baking pan, preferably metal, with nonstick cooking oil spray or room-temperature unsalted butter. Line with parchment paper, leaving a handle on all sides. (If you have a precut sheet of parchment, simply slice it in half crosswise, then overlap the halves to line the pan.) Lightly coat parchment with nonstick spray.
Assemble your makeshift double boiler (this is a method for gently cooking sensitive ingredients). Gather a medium saucepan and 2 medium heatproof bowls that can sit over the saucepan without dipping too far into it. Pour water into saucepan to come 1" up the sides (there should be a gap between the water and bowl so check it before the water gets hot!) and bring to a simmer over medium heat. Cut 8 oz. cream cheese (not low-fat) into 1" pieces and place in one of the medium bowls; set over saucepan. Heat cream cheese, stirring occasionally, until very soft, about 5 minutes. You want it to be soft enough that you can easily mix it with a heatproof rubber spatula or wooden spoon.
Remove bowl from heat (leave water simmering). Mix cream cheese until smooth. Add 1 chilled large egg, ⅓ cup (66 g) sugar, ½ tsp. vanilla extract, and ¼ tsp. kosher salt and whisk until very smooth. Transfer about half of cream cheese mixture to a small bowl (it’s fine to eyeball it) and whisk in 1½ tsp. unsweetened cocoa powder. (Both Dutch-process and natural cocoa powder will work in this recipe, but the former will provide a deeper color and a smoother, richer flavor.) Set both bowls of cream cheese mixture aside.
Cut 10 Tbsp. unsalted butter (142 grams) into 1" pieces. Place in the remaining medium heatproof bowl. Add 1 tsp. instant espresso powder (if using) and remaining 1 cup (200 g) sugar, ¾ cup plus 2 Tbsp. cocoa powder (80 g—break up big lumps before measuring as they will throw off your weight and you want to be as precise as possible here), and ½ tsp. kosher salt.
Place bowl over saucepan of still simmering water and cook, stirring occasionally once the butter starts to melt, until mixture is homogeneous and too hot to leave your finger in it, 7–9 minutes. Let cool 5 minutes. Don't panic if your batter looks stiff or otherwise wrong at this point—once you do the next step, it'll return to a glossy, beautiful mixture.
Add remaining 2 chilled large eggs and remaining ½ tsp. vanilla extract to butter mixture one at a time, whisking vigorously after each addition until smooth and glossy (the mixture will look curdled and broken until you add the second egg). Add ½ cup (63 g) all-purpose flour and mix with spatula or spoon until no longer visible, then vigorously mix another 30 strokes. Consider this recipe your arm workout! Why are the eggs chilled? Because it helps the batter to emulsify, ensuring the fat doesn't separate.
Scoop out ½ cup brownie batter and set aside (place near a warm spot, like the oven, to keep it loose). Scrape remaining batter into prepared pan and spread into an even layer. Working quickly, spoon alternating dollops of cocoa–cream cheese mixture and cream cheese mixture over batter. Dollop reserved brownie batter on top (it will be quite thick). Don’t worry if your design looks random and spotted.
Bake brownies until center is set and no longer looks wet (the chocolate blobs will change from glossy and shiny to matte), 22–25 minutes. (If you're using a glass pan, this might take significantly longer, so use a toothpick to check that only a few moist crumbs are pulled out.) Brownies may have puffed—they'll deflate as the cool. Transfer pan to a wire rack and let cool completely. Using parchment paper overhang, lift brownies out of pan and transfer to a cutting board. Remove parchment paper and cut brownies into sixteen 2¼" squares, wiping knife clean with a damp rag between slices. To easily cut even squares, cut the brownies into four quadrants, then slice each quadrant in four.