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1
To make a sugar syrup, whisk together the sugar and water in a small saucepan, place over medium heat, and bring to a boil.
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2
Boil for about 30 seconds, or until the sugar dissolves and the mixture is clear.
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3
Remove from the heat and let cool completely before using.
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4
(This syrup may be made days, or even weeks, in advance and stored in a tightly covered jar in the refrigerator.)
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5
In a bowl, stir together the sugar syrup, tangerine juice, and 6 tablespoons lime juice.
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6
Taste and add more lime juice if needed to create a strong sweet-tart balance.
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7
Strain through a fine-mesh sieve positioned over a bowl.
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8
Cover with plastic wrap and refrigerate for at least 24 hours to chill well and develop the flavor.
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9
Freeze the mixture in an ice-cream maker according to the manufacturers directions.
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10
Prepare the base a day or two in advance of churning and let it chill and develop flavor in the refrigerator.
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11
Churn the sorbet or ice cream at least 2 hours before serving, pack tightly into a container to prevent crystallization, and place in the freezer to firm up and smooth.
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12
Let the sorbet or ice cream stand at room temperature for about 15 minutes to soften before serving.
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13
The flavor of a sorbet or ice cream fades after 3 or 4 days.
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14
To revive it, thaw it until it is once again a liquid, make any flavor adjustments, and refreeze in an ice-cream maker.
