Preheat your oven to 350°F and line a 9x13 inch baking pan with parchment paper, allowing some overhang for easy removal. While the oven preheats, whisk together the flour, cocoa powder, espresso powder, salt, and baking powder in a medium bowl. Set this dry mixture aside—having it ready will let you work quickly once you start combining the wet ingredients.
Cut the butter into chunks and place it in a small saucepan over medium heat. Let it cook for 10-12 minutes, swirling occasionally, until the milk solids turn golden brown and the butter smells nutty and rich. Pour the browned butter into a large mixing bowl, then immediately add the chocolate chips and let them sit for 1-2 minutes to begin melting. Stir gently until the chocolate is completely smooth and glossy—the residual heat will melt everything without scorching it. I find that browned butter adds a deeper, more sophisticated flavor than regular melted butter, which really complements the espresso.
In a separate medium bowl, whisk together the room-temperature eggs, sugar, and vanilla extract for 1-2 minutes until the mixture is pale, slightly thickened, and ribbons fall from the whisk. Room-temperature eggs whisk more efficiently and incorporate more air, which helps create a fudgy yet tender crumb.
Pour the whisked egg mixture from Step 3 into the bowl with the browned butter and melted chocolate from Step 2. Stir gently and thoroughly until the mixture is smooth and well combined, taking care not to deflate all the air you just whisked in. The batter should look glossy and uniform.
Add the dry ingredient mixture from Step 1 to the wet mixture. Using a spatula, fold gently until just combined—stop as soon as you don't see any flour streaks. Overmixing develops gluten and can make brownies tough, so I always fold rather than stir to keep them tender and fudgy.
Pour the batter into the prepared pan from Step 1 and smooth the top with a spatula. Bake for 30-40 minutes, until a toothpick inserted into the center comes out with a few moist crumbs (not wet batter, but not completely clean either). The brownies will continue to cook slightly as they cool, so it's better to slightly underbake than overbake for that fudgy texture.
Let the brownies cool in the pan for at least 15-20 minutes before cutting—they'll be easier to cut cleanly and less crumbly. Use the parchment paper overhang to lift the entire brownie block out of the pan onto a cutting board, then cut into squares with a sharp knife wiped clean between cuts for neat edges.