Peel the peaches, being careful to remove only the skin. Then halve the peaches and remove the pits. Chop the peaches coarsely and place them in a large mixing bowl. Crush them with a masher.
Add the cream or milk and stir. Add sugar a little at a time and taste, adding more if desired. Add the lemon juice, vanilla and fine salt. Add the zest to the mixture and stir.
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.
A viewer or guest of the show, who may not be a professional cook, provided this recipe. It has not been tested for home use.