CHEESECAKE: Preheat the oven to 325°. In a large bowl, beat the cream cheese and sugar at medium speed until smooth. Beat in the eggs, 1 at a time, then beat in the sour cream. Pour the batter into six 5-ounce ramekins or custard cups.
Set the ramekins in a small pan and set the pan in the center of the oven. Add enough hot water to the pan to reach halfway up the sides of the ramekins. Bake the cheesecakes for 10 minutes, until set at the edges but still quite jiggly in the center. Turn off the oven and leave the cheesecakes in for 1 hour. Transfer the ramekins to a rack and let cool completely.
CARAMEL: In a heavy medium saucepan, heat the corn syrup. Stir in the sugar and cook over moderately high heat, undisturbed, until a deep amber caramel forms, about 9 minutes. Off the heat, carefully stir in the butter with a long-handled wooden spoon. Stir in the cream in a thin stream. Transfer the caramel to a heatproof pitcher and let cool. Stir in 3/4 teaspoon of fleur de sel.
Pour 1 1/2 tablespoons of the caramel over each cheesecake and swirl to coat the tops. If the caramel is too thick, warm it in a microwave oven at 10-second intervals. Refrigerate the cheesecakes until chilled, at least 3 hours. Sprinkle with fleur de sel just before serving.