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Special equipment: a deep-fry thermometer, a piping bag and a round ladle
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For the funnel cake: Pour the oil in a heavy stockpot and heat until a deep-fry thermometer inserted in the oil registers 375 degrees F.
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Meanwhile, in the bowl of a stand mixer or with a handheld electric mixer, beat the sugar and eggs together.
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With the mixer on low, add the milk slowly and mix to combine.
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Add the flour, baking powder and salt and beat until smooth.
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Pour the batter into a piping bag.
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Slightly submerge a round ladle in the hot oil and pipe the batter into the ladle (this will create the round look of the brain).
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Cook until slightly brown, 3 to 4 minutes, then transfer to a paper towel to drain.
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Continue with the remaining batter.
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For the pomegranate glaze: Put the pomegranate juice, cinnamon stick, orange zest and vanilla in a saucepan and bring to a boil.
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Lower the heat and cook at a slow boil until reduced by one-third, 12 to 14 minutes.
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Strain and let cool.
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For the walnut cream: Bring the cream, sugar and vanilla to a boil in a saucepan.
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Add the egg yolks and cook, whisking, until slightly thickened.
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Add a splash of cognac to taste.
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Strain the mixture into a bowl and cool in an ice bath.
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Stir the crushed walnuts into the cooled cream.
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To assemble, glaze the warm funnel cakes with the pomegranate glaze and serve on top of the walnut cream.