Both the cooked peaches and the custard mixture must be cooled to 40º before you churn them. Since they are fine in the refrigerator overnight, you may want to prepare them the day before you plan to churn and serve the ice cream. You'll get the very best results from using in-season, fully ripened peaches, but in a pinch, you can substitute 2 cups IQF (Individually quick frozen) sliced peaches and replace the vodka with peach-flavored liqueur. The ice cream is at it's peak when eaten within 4 hours of churning, although covered, it will keep in the freezer for up to two days. Adapted from the America's Test Kitchens. Prep time includes chill time. Cook time includes 2 hours of freezer time after churning.
Stir peaches, lemon juice, a pinch salt, and 1/2 cup sugar in medium-size nonreactive saucepan to combine; let stand until a pool of syrupy liquid accumulates and peaches soften slightly, 1 to 1 1/2 hours.
Position sieve over medium bowl set in an ice-water bath; set aside. Heat milk, cream, and 1/2 cup sugar in medium-size heavy saucepan over medium heat, stirring occasionally, until steam appears, 5 to 6 minutes. Turn off heat. Meanwhile, whisk yolks and remaining 6 tablespoons sugar in medium bowl until pale yellow. Stir half the warmed milk mixture into beaten yolk mixture until just blended. Return milk-yolk mixture to saucepan of remaining warmed milk mixture. Heat milk-yolk mixture over medium-low heat, stirring constantly with wooden spoon until steam appears, foam subsides, and mixture just begins to thicken or instant-read thermometer registers 180 degrees (mixture must not boil or eggs will curdle). Remove from heat, immediately strain custard into prepared bowl. Cool custard mixture to room temperature, stir in vanilla, then cover and refrigerate until instant-read thermometer registers 40 degrees, at least 2 and up to 24 hours.
Meanwhile, heat softened peaches and their liquid, stirring occasionally, over medium-high heat until peaches are tender and flesh has broken down, 3 to 4 minutes. Transfer to bowl, stir in vodka, and refrigerate until cold, at least 4 and up to 24 hours.
Strain chilled peaches, reserving liquid. Stir reserved peach liquid into chilled custard mixture; pour into ice cream machine canister and churn, following manufacturer’s instructions, until mixture is frozen and resembles soft-serve ice cream, 25 to 30 minutes. Add peaches; continue to churn until combined, about 30 seconds longer. Transfer ice cream to airtight container. Freeze until firm, about 2 hours.
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