Line a 10-inch square baking pan with foil or parchment, leaving an overhang on two sides for easy removal. Lightly coat with nonstick cooking spray.
Add the chocolate chips and butter to a microwave-safe bowl. Microwave in 20- to 30-second intervals, stirring between each, until the chocolate is melted and smooth. Set aside to cool until just warm, about 5-10 minutes.
In a large mixing bowl or the bowl of a stand mixer fitted with the whisk or paddle attachment, beat the eggs and granulated sugar on medium speed until pale, thick, and slightly increased in volume, about 3-5 minutes.
With the mixer on low, slowly pour in the slightly cooled chocolate mixture and mix just until combined.
In a separate bowl, sift together the cocoa, flour, baking powder, and salt.
Add the dry ingredients to the chocolate mixture in two additions, mixing on low speed just until no dry streaks remain. The batter will be thick.
Scrape the brownie batter into the prepared pan and use an offset spatula to spread it into an even layer, smoothing the top.