Preheat the oven Preheat your oven to 180°C / 350°F. Lightly grease a small baking dish. Place the dish inside a larger roasting pan (this will be used for a water bath later).
Melt the butter Melt the butter gently and set it aside to cool until warm, not hot.
Whip eggs and sugar In a large mixing bowl, combine the eggs and sugar. Using a hand mixer on high speed, beat for 5–8 minutes until the mixture becomes very thick, pale, and airy.
Add dry ingredients Sift the cocoa powder and flour together. Add them to the egg mixture along with the vanilla extract. Mix on low speed just until combined.
Incorporate the butter With the mixer still on low, slowly pour in the melted butter. Mix only until smooth, do not overmix.
Prepare the water bath Pour the batter into the prepared baking dish. Carefully pour hot tap water into the larger pan until it reaches about halfway up the sides of the baking dish.
Bake Bake for 55–60 minutes. The top should form a thin, brownie-like crust while the inside remains soft and pudding-like. A cake tester inserted about 2 inches from the edge should come out mostly clean; the center will look underbaked, that’s expected.
Serve Let cool slightly, then serve warm. Perfect with vanilla ice cream or softly whipped cream for contrast.
