In a small heavy saucepan, combine the apricots, 2 tablespoons of the sugar and 2/3 cup water. Bring to a boil over moderate heat
Reduce the heat to moderately low and simmer, uncovered, until the apricots are tender about 10 to 12 minutes
Transfer the apricots and any remaining liquid to a food processor and purée until smooth. Set aside
In a heavy medium saucepan, combine the milk and the heavy cream, remaining 1/3 cup sugar and salt
Cook over moderate heat, stirring frequently with a wooden spoon, until the sugar is completely dissolved and the mixture is hot, 5 to 6 minutes. Remove from the heat
In a medium bowl, whisk the egg yolks until blended. Gradually whisk in one-third of the hot cream in a thin stream, then whisk the mixture back into the remaining cream in the saucepan
Cook over moderately low heat, stirring constantly, until the custard lightly coats the back of the spoon, 5 to 7 minutes; do not let boil
Immediately remove from the heat and strain the custard into a medium bowl. Set the bowl in a larger bowl of ice and water. Let the custard cool to room temperature, stirring occasionally
Whisk in the reserved apricot purée. Cover and refrigerate until cold. Pour the custard into an ice cream maker and freeze according to the manufacturer's instructions.
