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1
Bring sugar and 1 cup water to a boil in a 2 1/2- to 3-quart heavy saucepan over moderately high heat, stirring until sugar is dissolved.
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2
Add apricots, then reduce heat and simmer, covered, until plump and very soft, 25 to 30 minutes.
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3
Drain apricots in a sieve set over a bowl, then return syrup to pan.
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4
Cook syrup over moderate heat, swirling pan occasionally, until a deep caramel, 4 to 5 minutes.
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5
(Syrup will bubble, so remove from heat periodically to check color.)
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6
Carefully add 1/2 cup water to caramel (mixture will bubble up and steam vigorously), then cook over moderate heat, stirring, until caramel is dissolved.
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7
Puree apricots and caramel in a food processor until almost smooth, then cool to room temperature.
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8
Whisk together apricot puree and yogurt in a large bowl until combined well and chill, covered, until cold, about 4 hours.
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9
Sprinkle gelatin over remaining 1/4 cup water in a very small saucepan and let stand 1 minute to soften.
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10
Heat gelatin over moderate heat, stirring, until dissolved, then immediately whisk into apricot mixture.
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11
Freeze apricot mixture in ice cream maker.
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12
Transfer to an airtight container and put in freezer to harden.
