Follow the instructions for your ice cream maker ( I am using a Cuisinart Pure Indulgence Ice Cream Maker)
Pour the cream mixture into the freezer bowl, while it is churning.
Once you see that the mixture is beginning to thicken add the chilled peach mixture.
Allow the machine to continue churning until almost fully thickened. (about 20 mins)
Slowly add the cut pieces of peaches during the final couple of minutes.
Churn for a couple more minutes, just until the pieces a distributed throughout the ice cream.
Turn off the machine and serve or transfer the ice cream to a freezer container.