Cook the Cherries: Wash the cherries thoroughly, remove the stems, and pit them.
In a large enameled pot, combine the pitted cherries, sugar, and water.
Bring the mixture to a boil over medium-high heat, then reduce the heat and let it simmer for 15 to 20 minutes, until the cherries are soft.
Create the Soup Base: Carefully drain the cherries, making sure to reserve all of the cooking liquid in a separate bowl.
Set aside 24 of the best-looking whole cherries for garnish. Press the remaining cooked cherries through a fine-mesh sieve into the reserved liquid, using the back of a spoon to extract as much pulp as possible.
Discard the skins.
Flavor and Chill: Return the purée and liquid to the pot.
Stir in the white wine and fresh lemon juice.
Taste the soup and adjust the seasoning, adding a bit more sugar for sweetness or lemon juice for brightness.
Cover and chill the soup in the refrigerator for at least 4 hours, or until it is completely cold.
Assemble and Serve: Just before serving, whip the cold heavy cream in a separate bowl until soft peaks form—do not add any sugar.
Place 4 of the reserved whole cherries into the bottom of each of 6 chilled bowls. Ladle the cold soup evenly over the cherries.
Top each serving with a generous dollop of the unsweetened whipped cream and serve immediately.