In a large bowl, combine the sliced peaches and granulated sugar, then let them sit for 15 minutes to macerate.

While the peaches macerate, whisk together the heavy cream, whole milk, and vanilla extract in a separate bowl.

Puree half of the macerated peaches in a blender or food processor until smooth, then dice the remaining peaches into small pieces.

Combine the pureed peaches, diced peaches, and the cream mixture, stirring well.

Pour the mixture into an ice cream maker and churn according to the manufacturer's instructions until it reaches a soft-serve consistency.

Transfer the ice cream to an airtight container and freeze for at least 2-4 hours, or until firm, before serving.