Preheat the oven and prepare the dish

• Preheat the oven to 180 °C top/bottom heat.
• Grease an 8-inch baking dish and set it aside.

Melt the butter

• Melt the butter, then let it cool slightly.

Whip the eggs and sugar

• Beat the eggs and sugar with a hand mixer on high speed until very thick and light yellow.

Add the dry ingredients and vanilla

• Sift the cocoa powder and flour.
• Add the vanilla extract to the egg mixture, then gently mix in the sifted dry ingredients on low speed.

Incorporate the melted butter

• Still on low speed, slowly pour in the melted butter and mix until just combined. Do not overmix.

Set up the water bath

• Pour the batter into the prepared baking dish.
• Place the dish inside a larger pan and pour hot tap water into the larger pan until it comes about halfway up the sides of the baking dish.

Bake

• Bake for exactly 1 hour: the top will form a crisp brownie-like crust while the inside stays soft and pudding-like.
• A cake tester inserted about 2 inches from the side should come out about three-quarters clean; the center will look under-baked, which is normal.

Cool and serve

• Let cool slightly, then serve warm with vanilla ice cream or whipped cream.