Preheat oven to 350F (175C). Line an 8x8 metal baking pan¹ with parchment paper (use enough that some is hanging over the sides so you can lift the brownies out of the pan easily after baking and cooling). Set aside.
In a microwave-safe bowl, combine butter pieces and chocolate chips. Microwave for 20-second increments, stirring well in-between, until chocolate and butter are completely smooth and melted. Set aside.
In a separate bowl, use an electric mixer (or stand mixer) to beat together the eggs, sugar, and vanilla extract until mixture is pale and fluffy and increased in volume (this will probably take at least a minute, maybe longer, on high speed).
Sift cocoa powder, cornstarch, and salt into egg mixture and then fold ingredients together until combined with a spatula (if you don’t have a sifter, just whisk them together in a separate bowl to remove any lumps before stirring into egg mixture).
Drizzle the melted butter/chocolate mixture into the batter and use a spatula to gently stir until just combined.
Transfer to prepared baking pan and bake on 350F (175C) for 35 minutes or until a knife inserted in the center comes out clean.
Allow brownies to cool completely before lifting out of the pan using the parchment paper and slicing and serving (if they're still warm they will definitely fall apart).
¹You can bake these in a 9x9 metal baking pan instead, they will need about 25-30 minutes to bake.