Preheat oven to 350 degrees F. Grease an 8-inch square pan and line with parchment paper or foil.
Melt the butter in a microwave-safe bowl or small saucepan. Add the cocoa powder and stir until smooth.
Add the sugar and return to heat for about 30 seconds, then stir to dissolve sugar. Let stand for 5 minutes.
With a whisk or a heavy duty scraper, add the eggs one at a time, beating vigorously after each addition. Whisk or stir in the vanilla.
Stir in the flour. If mixture is warm, let cool slightly, then add some of the chocolate chips.
Scrape the batter into the prepared pan, spread evenly, and sprinkle remaining chocolate chips on the top. Tap the pan lightly on the counter to bring air bubbles to the top.
Bake for about 35 minutes. The batter will rise to the top of the pan and the brownies will be very jiggly and appear underdone. You can pull them at 35 minutes at which point the internal temperature should be at 205 and a meat thermometer probe will have very fudgy almost batter-like brownie on it, not moist crumbs. This is due to the eggs. The brownies should set up as they cool.
Let cool for about 20 minutes at room temperature, then remove from the pan and transfer to the freezer to finish cooling. Remove from the freezer and slice while partially frozen. Or just leave them alone until you are ready to slice them. They hold together well, the freezer just speeds things up.