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Place eggs, milk, cream and orange zest in a large mixing bowl. Using a fork, whisk until well combined.
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Slice the hot cross buns in half lengthways and dip each half into the mixture, coating both sides well.
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Leave in the mixture to soak for 15–20 minutes.
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Heat a frying pan over medium heat. Add the olive oil and carefully swirl it around to coat the pan evenly.
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Remove hot cross buns from the mixture, allowing any excess beaten egg to drip off.
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Cook in batches by placing coated buns on the frying pan and cooking for two minutes each side or until golden brown. Transfer to serving plates.
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Repeat with remaining oil and hot cross bun halves.
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To serve, add a spoonful of ice cream, honey or maple syrup and fruit of your choice.