Peel and pit the peaches. Finely dice 0.5 cup and set aside; chop the remaining peaches.
Combine the chopped peaches with 0.5 cup sugar and the lemon juice in a saucepan. Let macerate until juicy, 20–30 minutes, then cook over medium heat, stirring, until softened and syrupy, 5–7 minutes. Cool to room temperature, then puree until smooth; chill.
Warm the whole milk, remaining 0.5 cup sugar, and the kosher salt in a medium saucepan over medium heat until steaming and the sugar dissolves; do not boil.
In a bowl, whisk the egg yolks until smooth. Slowly whisk in about half the hot milk to temper, then return the mixture to the saucepan. Cook over medium-low, stirring constantly with a spatula, until the custard thickens to nappe and reaches 170–175°F, 5–8 minutes.
Strain the custard through a fine-mesh sieve into a clean bowl. Stir in the heavy cream and vanilla, then whisk in the cooled peach puree. Chill until very cold, at least 4 hours or overnight.
Churn the mixture in an ice cream maker according to manufacturer’s instructions until it reaches soft-serve consistency and has increased in volume, 20–25 minutes. In the last minute of churning, add the reserved diced peaches.
Transfer to a freezer-safe container, press parchment or plastic wrap directly on the surface, and freeze until firm, 3–4 hours. Scoop and serve.