Preheat oven to 350 F and line a 9x9 baking pan with parchment paper. Allow parchment to hang over the side to use as handles later.
Pour melted butter over chocolate chips in a bowl and allow to sit for a minute to soften chocolate. Stir with wooden spoon.
Add eggs, cocoa, sugar and vanilla and stir.
Stir in the flour just until no more traces of flour remain.
Scrape the batter into the prepared pan. Bake for 30 minutes, or until a toothpick inserted in the center comes out clean.
Allow brownies to cool in pan for at least five minutes. Use the parchment handles to lift the brownies out and onto a cooling rack. Allow to cool completely before cutting.
Notes
I know it's really hard to resist, but brownies really need to cool before cutting them.
Don't over mix the batter. Use a wooden spoon instead of a hand mixer and only stir until all dry traces are gone.
Ovens may vary, so use the toothpick test in the middle after 30 minutes.