Preheat your oven to 325°F. Line an 8x8 metal pan with parchment paper and set it aside.
In a small bowl, whisk together the cake flour, cocoa powder, baking powder, and salt. Set aside.
In a medium saucepan, melt the butter over medium heat. Add the chocolate chips and stir until smooth. Remove from the heat and let it cool slightly.
In a medium bowl, combine the eggs, egg yolks, granulated sugar, and brown sugar. Whisk by hand or with an electric hand mixer for about 1-2 minutes, until foamy and slightly lighter in color.
While whisking the egg and sugar mixture, slowly stream in the melted butter and chocolate. Whisk until fully combined.
In a small bowl or cup, stir the espresso powder and vanilla extract into ¼ cup of hot water. Add this to the egg mixture and whisk to combine.
Sift the dry ingredients over the wet mixture, then gently fold in using a spatula until just combined.
Pour the batter into the prepared pan and spread it out evenly.
Bake in the preheated oven for 30-35 minutes, or until the edges are slightly cracked and the center is set (it shouldn’t jiggle). A toothpick inserted into the center should come out with fudgy crumbs, not dry. Allow the brownies to cool completely before cutting for clean slices.