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1
Roll the oranges on a work surface to loosen them slightly.
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2
Halve the oranges horizontally and use a spoon to scoop out all of the flesh, being careful to keep the skins intact.
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3
Put the orange flesh in a food processor.
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4
Arrange the shells on a baking sheet and set aside.
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5
Puree the orange flesh and press through a sieve; you should have 2 1/4 to 2 3/4 cups of juice.
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6
Set aside.
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7
Combine the lemon juice, sugar, honey and water in a medium saucepan and simmer over medium heat until reduced to 1 1/2 cups, about 45 minutes.
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8
Let cool.
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9
Whip the egg white until it forms soft peaks and whisk in the orange juice.
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10
Whisk in the honey mixture.
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11
Refrigerate until cold.
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12
Freeze in an ice cream machine according to the manufacturer's instructions.
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13
Place in a bowl, drizzle the Campari over the sorbet and fold it in just enough to form streaks; do not overmix.
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14
Working quickly, fill the orange shells to the top with sorbet; you won't use all of the shells.
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15
Cover with plastic wrap and freeze until very firm, at least 2 hours.
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16
To serve, use a large serrated knife to cut each orange shell into 3 wedges.
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17
Arrange the orange wedges on plates and garnish with a sprig of mint.
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18
Serve immediately.
