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Preheat the oven to 350 F. Bring a full kettle of water to boil.
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Butter six 4-ounce ramekins and dust with sugar, set aside.
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Bring the milk to a simmer in a small saucepan.
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Meanwhile, melt the butter in a medium saucepan over medium heat. Add the flour and cocoa powder to the butter, whisking until it has a smooth paste-like consistency. Reduce the heat to low and cook for 1 minute.
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Slowly add the hot milk to the butter mixture, whisking until smooth. Whisk in the melted chocolate. Remove from the heat and let cool for 5 minutes. Lightly whisk the egg yolks and then stir them into the mixture.
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In a medium bowl, beat the egg whites until frothy. Slowly add the sugar, one tablespoon at a time, and beat until the egg whites form stiff, glossy peaks. Stir a heaping spoonful of egg white mixture into the chocolate mixture, then fold in the remaining egg whites until just combined.
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Pour the soufflé batter into the prepared ramekins. Place the ramekins in the large cake pan and add enough boiling water to reach halfway up the sides of the ramekins.
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Bake for 20 minutes. Don’t open the oven while the soufflés are baking.
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Once baked, place the ramekins on a wire rack to cool slightly. Serve warm with the vanilla sauce.