Chill a mixing bowl and beaters. For crust, line the bottom of a 9-inch springform pan with ladyfingers, cutting to fill spaces. Trim bottoms of the remaining ladyfingers slightly to stand in pan. Place ladyfingers, round side out, against pan sides. Set aside.
For cream cheese filling, beat cream cheese and granulated sugar with an electric mixer on medium speed until combined. In the chilled bowl beat 1-3/4 cups of the whipping cream and the powdered sugar until soft peaks form; set aside 1/2 cup of the whipped cream mixture. Fold remaining whipped cream mixture into cream cheese mixture.
For pumpkin filling, stir together pudding mixes, cinnamon, ginger, and pie spice. Add pumpkin and milk; beat until thick. Fold in reserved whipped cream mixture.
Spread the cream cheese filling evenly onto the bottom of prepared pan. Carefully spread pumpkin layer over cream cheese layer. Cover and refrigerate overnight.
To serve, remove side from pan; place charlotte on a platter. If desired, brush side with melted jam. Beat remaining whipping cream to soft peaks; spoon some atop each serving. If desired, sprinkle with additional pumpkin pie spice. Makes 12 servings.