Allow your peaches to thaw overnight in the fridge. Toss peaches with ½ cup of sugar and set aside for 15-20 minutes.
Reserve ½ cup of the peaches, but without the juice. Blend the remaining peaches with the juice in a food blender, and set aside.
Prepare the base:
Make the creamy base: In a large bowl, whisk the remaining sugar, heavy cream, milk, vanilla, and peach extract, if you are using one.
Stir in the peach puree until well combined.
Churn and freeze:
Churn the ice cream according to your manufacturer's directions. In the last five minutes, add the reserved chopped peaches. You will get a soft serve with this. If you want firmer ice cream, transfer the peach ice cream into a freezer-friendly container, cover it with plastic wrap, and refrigerate for 4 hours or overnight.