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1
Cook sugar and salt in a dry 4- to 5-quart heavy pot over moderate heat, undisturbed, until it begins to melt. Continue to cook, stirring occasionally with a long-handled wooden spoon, until sugar is melted into a deep golden caramel, 10 to 12 minutes.
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2
Carefully pour in cream (caramel will harden and steam vigorously). Simmer over moderately low heat, stirring occasionally, until caramel is dissolved. Whisk in milk and return just to a boil, then remove from heat.
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3
Whisk together yolks and corn syrup in a large bowl until smooth, then add half of hot caramel cream in a slow stream, whisking until combined well. Add yolk mixture in a slow stream to caramel cream in pot, whisking, then cook over low heat, stirring constantly with wooden spoon, until mixture is thickened and thermometer registers 170 to 175u00b0F, about 3 minutes.
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4
Immediately pour caramel custard through a fine-mesh sieve into a metal bowl set in a larger bowl of ice and cold water. Cool to room temperature, stirring occasionally, about 20 minutes.
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5
Remove custard from ice bath and chill, covered, until cold, about 1 hour. Freeze in an ice cream maker, then transfer to an airtight container and put in freezer to harden, at least 4 hours.
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6
Sprinkle scoops of ice cream with sea salt if desired.
