Pour the peach mixture into the canister of your ice cream machine and cover the top securely. Place the canister carefully in the machine, and then pack layers of crushed ice and kosher salt around the canister, until it is surrounded almost to the top. Place the motor on top of the machine and start it. Let the machine run for about 20 minutes, until the ice cream is finished churning and the machine slows.
Remove the canister from the machine, being careful not to let any ice or salt into it. Spoon the mixture into a freezer-proof bowl and cover it with plastic wrap. Place the bowl in the freezer until the ice cream hardens, about 6 hours.