Bring 1 litre of water to the boil, and cook carrots until very tender, about 45 minutes. Drain cooked carrots. Return them to a moderate heat for a minute or so to cook off excess moisture.
Preheat oven to 200 C / Gas 6. In a medium bowl, combine digestive biscuit crumbs, ginger nut crumbs, ground pecan nuts and sugar; toss well. Rub in butter until mixture is crumbly. Pat over bottom and up sides of a buttered 23cm springform cake tin. Bake the base for 7 minutes. Decrease oven temperature to 180 C / Gas 4.
Transfer carrots to food processor and puree for 30 seconds. Scrape down side, and puree again until absolutely smooth. Add dark brown soft sugar, ginger, lemon juice, orange zest, cinnamon, mace and allspice to the processor, and puree for 30 seconds. Scrape down sides, and repeat. Let mixture stand until cool.
Add cream cheese to cooled carrot mixture, and puree for 1 minute; scrape down sides every 20 seconds. Beat in eggs, one at a time. Pour mixture over the base, and sprinkle with remaining 60g of chopped pecans.
Bake for about 50 minutes; cake tester will come out clean. Let cool. Cover loosely, and refrigerate at least 4 hours before serving.