Fortunately, David Liebovitz has a recipe for peach ice cream in his book, The Perfect Scoop (which, by the way, is a great ice cream cook book).
1 1/3 pounds ripe peaches (~4 large peaches)
1/2 cup water
3/4 cup sugar
1/2 cup sour cream
1 cup heavy cream
1/4 tsp vanilla extract
a few drops freshly squeezed lemon juice
Peel the peaches*, slice them in half, and remove the pits. Cut the peaches up and put them in a saucepan. Add the water and cook over medium heat, covered, until they are soft and cooked through. This should take about 10 minutes.
Remove the pan from the heat, stir in the sugar, and then let it all cool to room temperature. Your kitchen should be smelling pretty amazing by now.
Puree the cooked peaches and any associated liquid, along with the sour cream, heavy cream, vanilla, and lemon juice until everything is almost smooth. You can do this in a blender or food processor. Just watch out that you don't fill your food processor over the "max fill line" like I did. It was a mess. Alternately, you can puree everything with an immersion blender (which is what I did).
Chill everything in the fridge for a few hours, then freeze it in your ice cream maker according to the manufacturer's directions. You can eat it as is, or if you'd prefer a firmer ice cream you can stash it in the freezer for a few hours before digging in. Enjoy the peachy goodness!
*How to peel peaches:
David Liebovitz offers a tip on how to easily peel your peaches. Start by cutting an X on the bottom of the peaches, then lower them into a pot of boiling water for about 20 seconds. Use a slotted spoon or ladle to transfer the peaches from the boiling water to a colander in the sink, and run some cold water over them. Once they cool a bit, you can slip their skins right off!