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Bake the Sponge
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Preheat the oven to 180°C / 350°F.
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Separate the eggs. Beat the egg whites until stiff while gradually adding the sugar. Once the mixture is glossy and thick, beat in the egg yolks.
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Sift together the flour and cornstarch and gently fold them into the batter in two or three batches.
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Pour the batter into a 26 cm (10-inch) springform pan lined with parchment paper and bake for about 35 minutes. Let the cake cool completely, then slice it horizontally into three layers.
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Prepare the Coconut Cream
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In a saucepan, simmer the coconut milk and shredded coconut over low heat for about 45 minutes until it reduces and becomes a thick coconut paste.
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Let the mixture cool slightly. Stir in the rum and chopped white chocolate until the chocolate melts completely.
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Chill the mixture in the refrigerator until it thickens.
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In a separate bowl, beat the mascarpone with powdered sugar until smooth. Fold the coconut-white chocolate mixture into the mascarpone and refrigerate until spreadable.
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Make the Strawberry Lemon Compote
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Puree about two-thirds of the strawberries with the lemon zest, lemon juice, vanilla, sugar and strawberry jam.
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Bring the mixture to a boil in a saucepan. Stir the cornstarch with a little cold water and add it to the strawberry mixture. Simmer briefly until thickened.
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Remove from heat and stir in the rum. Let cool completely.
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Assemble the Cake
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Place the first sponge layer on a cake plate and brush it lightly with the rum-orange juice mixture.
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Spread a layer of coconut mascarpone cream on top, followed by some strawberry compote.
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Repeat with the second sponge layer.
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Place the final cake layer on top and cover the entire cake with the remaining cream.
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Decorate
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Press shredded coconut around the sides of the cake.
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Decorate the top with whipped cream swirls and fresh strawberries.
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Chill the cake for at least 2 hours before serving so the layers set nicely.