3 medium ripe peaches, peeled, pitted, and cut into ½ inch pieces.
½ tsp lemon juice
pinch salt
1 c plus 6 tbs sugar, divided
1 ¼ c whole milk
1 1/3 c heavy cream
6 egg yolks
1 tsp vanilla
2 tbs vodka
Stir peaches, lemon juice, salt, and ½ c sugar in non-reactive saucepan to combine; let stand until a pool of syrupy liquid accumulates and peaches soften slightly, 1 to 1 ½ hours.
Position sieve over medium bowl set in an ice water bath; set aside
Heat milk, cream, and ½ c sugar in heavy saucepan over medium heat, stirring occasionally, until steam appears, 5 to 6 minutes. Turn off heat.
Whisk yolks and remaining 6 tbs sugar until pale yellow. Stir half the warmed milk mixture into the yolk mixture until just blended. Return milk-yolk mixture to saucepan of remaining milk,. Heat milk-yolk mixture over medium-low heat, stirring constantly with wooden spoon unti steam appears foam subsides, and mixture just begins to thicken, 180F. Do not boil or eggs will curdle. Remove from heat and immediately strain custard into prepared bowl. Cool custard to room temperature, stir in vanilla, then cover and refrigerate to 40F, 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 liquid into chilled custard; pour into ice cream machine and churn, 25 to 30 minutes. Add peaches; continue to churn until combined, about 30 seconds.