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.

Start the ice cream canister turning. Pour the peach mixture into the canister and cover the top securely.

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.