1 cup (about 6 ounces) dried apricots
1/3 cup plus 2 tablespoons granulated sugar
2/3 cup water
1 1/2 cups milk
2 tablespoons Earl Grey tea leaves
1 1/2 cups heavy cream
Pinch of salt
4 egg yolks
1 tablespoon apricot brandy or orange liqueur
In a small heavy saucepan, combine the apricots, 2 tablespoons of the sugar and water. Bring to a boil over moderate heat. Reduce the heat to moderately low and simmer, uncovered, until the apricots are tender, 10 to 12 minutes.
Transfer the apricots and any remaining liquid to a food processor and puree until smooth, scraping down the sides of the bowl once or twice. Set aside.
In a heavy medium saucepan, combine the milk and tea leaves. Warm over low heat until the milk is hot. Remove from the heat and let steep for 5 minutes. Strain the milk through a fine-meshed strainer.
Return the milk to the saucepan and add 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 puree and the brandy until blended. Cover and refrigerate until cold, at least 6 hours or overnight.
Pour the custard into an ice cream maker and freeze according to the manufacturer’s instructions.