Preheat the oven to 325 degrees F. Lightly grease a 9x13-inch pan (I use baking spray with flour, but butter or shortening will also work).
Sift together the flour and cocoa powder into a medium-sized bowl. In a separate large bowl, vigorously whisk together the eggs, egg yolk and sugar for around 20-30 seconds, until thick and pale in color (they should form a ribbon when the whisk is lifted, see notes).
Whisk the sifted ingredients into the egg mixture along with the salt and espresso powder, if using. Switch to a spatula and vigorously stir in the butter, vegetable oil, and vanilla extract until the batter is shiny and smooth.
Spread the batter evenly into the pan, then bake for 30 to 35 minutes. The brownies are done when a toothpick inserted into the center comes out clean; a few moist crumbs are fine, but there should be no visible raw batter.
Remove the pan from the oven and cool brownies completely before cutting.
Store in an airtight container for 5 days at room temperature, or freeze for up to 2 months.
My favorite cocoa powder is from Valrhona (I’m not paid to say this). It’s preferred by most chefs for a reason. You’ll get an incredibly rich chocolate flavor and dark color.
Espresso powder (such as this one from King Arthur Flour) enhances the chocolate flavor. It's not the same as ground espresso, so please don't substitute that. Espresso powder is completely optional, and it doesn’t make the brownies taste like coffee/espresso. It’s subtle.
Here's a video that shows how to whisk eggs and sugar until they form a ribbon.