Preheat oven to 325F. Spray a 2-quart baking dish with cooking spray.

Melt butter; set aside to cool.

In the bowl of a stand mixer fitted with the paddle attachment, beat the eggs and sugar on medium-high speed for 5 to 10 minutes, or until very thick and pale yellow in color (the batter will form ribbons off the paddle if you lift it).

Meanwhile, sift the cocoa powder and flour together into a separate bowl.

When the egg and sugar mixture is ready, turn the mixer down to low, and add the vanilla extract and cocoa/flour mixture, beating only until just combined. With the mixer still on low, pour in the melted and cooled butter and continue beating just until combined.

Spread the brownie mixture into the prepared dish. Place it inside a large roasting pan and add enough really hot tap water to the roasting pan to come about halfway up the sides of the baking dish. Bake for 50-60 minutes, or until a toothpick inserted about 2 inches from the edge comes out partially clean. (The center is going to look under-baked, the dessert is supposed to be gooey.)

Transfer the baking dish to a wire rack and let cool. Serve warm with ice cream or whipped cream!