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Using a small sharp knife, peel the oranges, removing all of the bitter white pith. Working over a large glass dish, cut between the membranes to release the orange sections. Arrange them in the dish and add any accumulated orange juice.
In a medium saucepan, combine the sugar, honey and 2 cups of water and bring to a boil over high heat, stirring until the sugar is dissolved. Pour the hot syrup over the oranges and let cool. Refrigerate until chilled, about 3 hours.
Spoon the oranges and syrup into 10 shallow soup plates. Pour 2 tablespoons of the Champagne into each bowl, garnish with mint leaves and serve.