Macerate the peaches: Peel peaches, dice into 1/2-inch chunks, and toss with 2 tablespoons sugar and lemon juice. Let sit at room temperature for 30 minutes, then mash half the peaches and refrigerate.
Heat the milk mixture: Combine milk, 1 cup of cream, and salt in a saucepan over medium heat until steaming (170°F), without boiling.
Whisk yolks and sugar: Vigorously whisk egg yolks and 1/2 cup sugar until pale and thickened, about 2 minutes.
Temper the eggs: Slowly pour hot milk into egg mixture while whisking constantly, then return the tempered mixture to the saucepan.
Cook the custard: Stir over medium-low heat until custard coats the back of a spoon and reaches 170-175°F (8-12 minutes). Do not boil.
Strain and cool: Strain custard through a fine mesh strainer into a clean bowl, stir in remaining cream and vanilla, then press plastic wrap on the surface and refrigerate for at least 4 hours or overnight.
Churn the ice cream: Pour chilled custard into the ice cream maker and churn for 20-25 minutes. Add peach mixture during the last 2-3 minutes of churning.
Freeze and serve: Transfer churned ice cream to an airtight container, press plastic wrap on the surface, seal, and freeze for at least 4 hours. Let soften 5 minutes before serving.