Prep your oven and pan. Position a rack in the center of the oven and preheat the oven to 350°F. Lightly spray a 9 x 13-inch cake pan with cooking spray and line with parchment paper, leaving a 2-inch overhang on the pan’s two long sides. Spray the parchment, too.
Mix the dry ingredients. In a medium bowl, whisk together the flour, cocoa powder, espresso powder, and salt.
Brown the butter, then add the chocolate. In a light-colored saucepan, melt the butter over medium-low heat, swirling the pan occasionally, until it starts to foam. Use a heatproof rubber spatula to scrape the bottom and sides of the pan occasionally to prevent the milk solids in the butter from burning. Cook for 5 minutes, or until the butter smells nutty and is amber with dark flecks at the bottom of the pan. Remove from the heat and immediately add the chopped chocolate. Stir with a rubber spatula until the chocolate is completely melted and combined. Pour the mixture into a liquid measuring cup. Set it on a wire rack to cool slightly while you prep the other ingredients.
Whisk the sugars, eggs, vanilla, then add the chocolate mixture. In the bowl of a stand mixer fitted with the whisk attachment, combine the sugars, eggs, and vanilla. Whisk on medium-high speed for 8 minutes, or until thick, fluffy, and doubled in volume. Reduce to low and slowly pour in the warm chocolate mixture, mixing on low speed until just combined.
Mix in the dry ingredients. Once the chocolate mixture is combined, use a rubber spatula to scrape down the whisk and the bottom and sides of the bowl. Affix the paddle attachment to the mixer and gradually add the dry ingredients, mixing on low speed until just combined.
Assemble the brownies. Pour the batter into the prepared pan and use an offset spatula to smooth the top. Bake the brownies. Bake for 35 to 40 minutes, or until a skewer inserted into the center of the brownies comes out with a few crumbs attached. Cool completely on a wire rack before slicing.
Serve and store. Run a butter knife or offset spatula along the edges of the pan and use the overhanging parchment as handles to lift the brownies out of the pan and onto a cutting board. Slice into 20 rectangles, each about 2 ¼ inches wide and 2 ½ inches long, and serve. The brownies can be stored in an airtight container or zip-top bag at room temperature for up to 3 days.