In a blender combine the frozen peaches and milk or cream. Blend until smooth, set aside.
For the Ice Cream:
In the bowl of a hand of stand mixer fitted with a whip attachment, whip the heavy whipping cream until stiff peaks form, 4-5 minutes. You can also do this by hand with a wire whisk, it will just take a little while.
In a separate mixing bowl combine the sweetened condensed milk, cinnamon, and vanilla extract, stir to combine. Gently fold the whipped cream into the sweetened condensed milk mixture. Continue folding until completely combined. Gently fold in the chopped peaches, and swirl in the peach puree.
Transfer the mixture into a loaf pan or similar container, freeze until solid, about 2 hours. Allow to sit at room temperature for a few minutes before scooping. This ice cream will keep in the freezer for up to two months!
Notes
**You can use any remaining heavy cream for the peach puree**You can use fresh or frozen peach chunks, if using frozen peaches, a 16 oz. bag of frozen peaches will work for this recipe.