Put the prunes in a small bowl and pour in cognac. Cover and chill overnight.
In a microwave-safe small bowl or glass measuring cup, microwave cream until barely simmering (do not let boil). Add tea, cover, and let steep off the heat 30 minutes. Strain into a bowl and set bowl in a larger one of ice and cold water. Once cool, cover and chill at least 1 hour.
In a microwave-safe bowl, heat butter with ginger just until butter melts. Cover and let steep 30 minutes.
Strain ginger butter into a bowl, pressing ginger against strainer. Discard ginger. Put 6 tbsp. ginger butter and the chocolate in a microwave-safe bowl. In 10-second bursts, microwave until two-thirds melted. Whisk to melt fully.
Preheat oven to 325°. In a separate bowl, whisk sugar, eggs, and salt together. Strain prunes (save cognac for cocktails).
Whisk chocolate-butter mixture into eggs and sugar. Stir in prunes.
Spoon batter into four 4-oz. ramekins or coffee cups, dividing evenly, then transfer to a small roasting pan. Carefully pour enough hot water into pan to come halfway up sides of ramekins. Cover pan tightly with foil.
Bake cakes until just set (when you gently touch center of a cake, your finger should come away clean), about 35 minutes. Let cakes cool on a rack until barely warm. Meanwhile, whip jasmine cream into soft peaks.
To serve, spoon some plum jam onto cakes and top with whipped cream and a sprinkle of toasted hazelnuts.
Make ahead: Jasmine cream through step 2, up to 1 day, chilled. Cakes, up to 2 days, cooled and then chilled. Let them come to room temperature before serving.
Wine pairing: A moderately sweet fortified red like Roxo 2011 Método Portugués "Ruby Tradicional" (Paso Robles; $48). --Sara Schneider