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Preheat oven to 175ºC/350ºF.
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Line and grease a 8 x 4in loaf tin.
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Zest one grapefruit.
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In a food processor using the metal blade mix sugar and grapefruit zest to allow the oils in the grapefruit to be released.
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Sift the flour, salt and baking powder into a bowl.
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In another bowl whisk eggs, sugar/grapefruit zest mixture, and vanilla.
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Slowly add the dry ingredients to the egg mixture.
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Fold in the vegetable oil and yogurt until fully incorporated.
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Pour batter into prepared loaf tin and bake for 40-50 minutes or until golden or until a cake tester inserted into the cake, comes out clean.
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Heat the grapefruit juice and tablespoon of sugar until sugar dissolves and liquid is clear. Set aside.
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Allow cake to cool in the tin for 10 minutes and then pour the liquid over the cake and allow to soak in.
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Remove cake from the pan and allow to rest on a baking sheet.
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To Make the Icing:
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Wtih an electric mixer, beat the cream cheese, grapefruit juice and butter together until light and creamy.
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Mix in the sifted powdered sugar, a little at a time, until incorporated.
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Spread icing over top of cooled cake in a thick layer.
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Garnish with grapefruit slices, or candied zest.
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Store in airtight container in the fridge.