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Mix together milk, cooking oil and salt in a bowl.
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Place the bowl over water bath and keep stirring until the mixture turns warm.
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Sieve cake flour into a bowl.
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Add flour to warm milk mixture and mix.
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Add egg yolks in batches and mix.
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Add vanilla extract and mix well.
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Beat egg whites until foamy.
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Add vinegar and castor sugar in batches and beat until firm peak.
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Transfer about ⅓ of the meringue to the egg yolk mixture and fold gently.
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Add finely grated parmesan cheese and fold in gently.
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Pour the mixture into the remaining meringue and mix gently with a whisk.
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Give the pan a few taps on a hard surface to release air bubbles.
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Line an 8 inch square pan with baking paper and pour in about half of the batter.
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Spread the batter in the pan evenly with a chopstick.
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Arrange slices of cheddar cheese to cover the batter but leave a small gap around the edges.
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Add the remaining batter and cover the cheese completely.
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Sprinkle finely grated parmesan cheese all over the top.
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Put the pan of batter into another slightly bigger pan.
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Place a tray of hot water at the bottom of an oven preheated to 160 C.
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Bake for 20 mins at 160 C and lower to 150C and bake for another 40 to 50 mins at the lowest rack of the oven.
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Test with a skewer and ensure that it comes out clean. Double check for doneness by pressing the surface of the cake gently with your finger or the back of a spoon. If it bounces back, the cake is fully cooked.
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Cut and serve while it is still hot from the oven. Cake could also be refrigerated. Thaw before serving.