If using fresh peaches, remove the pits, peel, and slice into quarters. If using frozen peaches, thaw on the counter for approximately 1 hour (or in the refrigerator overnight) until the peaches are nearly thawed.
Place peaches in a food processor, and pulse until the desired consistency is reached. (If you want smaller pieces of fruit in your ice cream, processes the peaches longer. If you prefer larger pieces of fruit, only pulse a few times.) Set aside.
In a medium bowl, whisk the sugar, salt, whole milk, and vanilla until most of the sugar is dissolved.
Add the heavy whipping cream, and stir again.
Carefully stir in the chopped peaches.
Set up your ice cream maker, and add the ice cream mix according to the manufacturer's directions. For this Cuisinart countertop model, assemble and turn on the ice cream maker, then add the ice cream mix.
Let churn until the ice cream freezes and thickens to the desired consistency (about 15 minutes).
Serve immediately, or transfer to a freezer-safe container (I like these Tovolo Glide-a-Scoop tubs). The ice cream will freeze to a harder consistency in 1-2 hours in the freezer.