Step 1

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.

Step 2

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 (see illustrations below) or instant-read thermometer registers 180 degrees (mixture must not boil or eggs will curdle). Remove from heat, and following step 3 in illustration, 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.

Step 3

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.

Step 4

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.