Place peaches in a large bowl and add 1/4 cup sugar, lemon juice, and salt. Let them sit undisturbed for 20 minutes. When they have softened, use a fork or potato masher to partially mash them, leaving a few diced pieces of peach. Set them aside.
Whisk the eggs, remaining ½ cup of sugar, and vanilla extract in a mixing bowl.
In a large saucepan, heat the whole milk over medium-low heat until warm. Slowly whisk the milk into the egg/sugar mixture, ¼ cup at a time. Be careful - if you add too much hot milk too quickly, the egg mixture will start to cook.
Return the mixture to the saucepan and add the heavy cream. Continue cooking over medium-low heat, stirring frequently until the cream begins to steam.
Remove the saucepan from heat and add the peaches and any accumulated juices; stir to combine. Place the saucepan in the freezer to chill for 1 hour.
Pour the mixture into the frozen insulated ice cream canister and churn according to product instructions.
After about 20-25 minutes, the ice cream will have a soft-serve texture. Place the ice cream canister in the freezer for about 2 hours to harden to the desired texture.