Adjust oven rack to lowest position and heat oven to 350 degrees F. Line a 9x13-inch baking pan with foil, leaving about a one-inch overhang on all sides. Spray with nonstick cooking spray.
Whisk cocoa powder and boiling water together in a large bowl until smooth. Add the unsweetened chocolate and whisk until the chocolate is melted. Whisk in the melted butter and oil (the mixture may look curdled at this point, that's okay!). Add the eggs, yolks, and vanilla extract, and whisk until smooth and homogeneous. Whisk in the sugar until fully incorporated. Add the flour and salt and mix with a rubber spatula until combined. Fold in the chocolate chips.
Scrape batter into prepared pan and spread into an even layer. Bake until a toothpick inserted halfway between edge and center comes out with just a few moist crumbs attached, 30 to 35 minutes. Transfer the pan to a wire rack and cool for 1½ hours.
Using the foil overhang, lift the brownies from pan. Place the brownies on the wire rack and cool completely, about 1 additional hour. Cut into 2-inch squares and serve. Brownies can be stored in an airtight container at room temperature for up to 4 days.