Preheat oven to 350°F (175°C). Line an 8×8-inch pan with parchment paper.
In a large mixing bowl, combine melted butter and sugar. Whisk until thoroughly blended and slightly glossy, indicating sugar begins to dissolve.
Add eggs one at a time, whisking well after each addition. Observe the mixture becoming lighter in color and slightly airy as eggs incorporate.
Stir in sifted cocoa powder and vanilla extract until fully integrated. The mixture will darken and thicken slightly, releasing a rich chocolate aroma.
In a separate bowl, whisk together flour, baking powder, and salt. Gradually add dry ingredients to the wet mixture, folding until just combined. The batter should be thick and slightly fudgy.
Gently fold in chocolate chips. Pour the batter into the prepared pan and spread evenly with a spatula. Bake for 25–30 minutes, until the edges are set and darker, and the center shows moist crumbs when tested.
Remove from oven and allow to cool in the pan for 10 minutes before transferring to a wire rack. The edges will be dark and caramelized, with a shiny, crackled surface, and the center soft and chewy.