Peel the peaches and dice them. In a small bowl, combine the chopped peaches with sugar and water and mash. You can use a fork if the peaches are really soft, or you can do what I did and use a potato masher - it worked great! You don't want to completely mash them, especially if you want some larger pieces of peaches in your ice cream.
Once the peaches are mashed, drain the mixture through a fine mesh strainer, reserving the juice. I strained the mixture several times to get most of the moisture out of it. You should have 3/4 cup of juice, but if you have a little bit less than that, add a little bit of water to bring the liquid to 3/4 cup. I usually have a little bit more, so I have to dump the extra juice out!
Combine the mashed peaches, the reserved juice and the sweetened condensed milk and mix with a spoon just until combined. Pour into a shallow pan - I use an 8X8 square pan. The shallower the pan, the faster the mixture will freeze. Freeze until firm - at least 3-4 hours.
Break the frozen mixture into chunks and place in a bowl for about 10-15 minutes to soften a little bit. Use an electric mixer to beat the mixture for several minutes. Whip a cup of whipping cream and fold it into the peach mixture. Pour back into the pan to freeze until firm before scooping and serving.