In a bowl, with your hands mix together the amaretti crumbs and butter to combine well. Press into the bottom of a 22 cm (9 in) spring-form pan. Bake in the middle of the oven until firm, about 12 minutes. Cool completely.
In a bowl, with a hand-held or stand mixer, beat the goat cheese for 3 minutes until smooth. Add the ricotta cheese, sugar, vanilla and salt and beat for 3 minutes until well blended. Add the eggs one at a time, beating well after each addition. Divide the mixture equally between 2 bowls. Fold the pumpkin puree, ginger and nutmeg into one bowl, and the melted white chocolate into the other.
Pour some of the white chocolate filling into the bottom of the pan to a depth of about 1 cm (1/2 in). Then, by large spoonfuls, alternately add the 2 fillings to fill the pan. Using a spatula, swirl the 2 batters slightly to marbleize. Place the cheesecake on a baking tray.
Reduce the oven temperature to 150°C (300°F) and bake the cheesecake for 45 minutes on the middle rack. Turn the oven off and leave the cheesecake inside for 2 hours more without opening the oven door. Remove the cheesecake and refrigerate for at least 6 hours before unmoulding.