Cut the ripe peaches into half inch wedges. Gently peel off the fuzzy peach peels.
Set out a medium mixing bowl. Add the peaches, lemon zest, and 5 tablespoons of sugar. Add a pinch of salt and mix well. Set aside.
Pour the cold heavy cream into a second bowl. Add 1 tablespoon of sugar and a teaspoon of vanilla extract. Use a handmixer with a whip attachment to lightly whip the heavy cream. It should be whipped and fluffy but still slightly pourable. (Not firm like whip cream you would pipe on top of the cake.)
Set out 4 large or 6 small serving cups. These can be glass ramekins or pedestal ice cream glasses. Spoon the peaches evenly into the cups. Make sure to pour the peach juices over the top.
Spoon the lightly whipped cream into the cups. Tap the cups gently so that the whipped cream works down in between the peaches.
Cover each glass with plastic then refrigerate for at least one hour, or up to two days. When ready to serve, remove the plastic and garnish the tops with additional lemon zest, a sprinkling of cinnamon, or with a vanilla wafer.
You can also make “peaches and cream” with fresh ripe nectarines or apricots.