Butter a 12-cup pudding mold. Fill a large pot fitted with a steamer insert with enough water to come halfway up mold (test this with an empty mold); set aside. Sift flour, spices, and salt in a bowl; set aside. Put Calvados and sultanas into a small saucepan. Bring to a simmer. Remove from heat; let stand 15 minutes. Drain; discard liquid. Set raisins aside.
Meanwhile, slice tops off persimmons. Scoop out flesh, and press through a sieve into a bowl, discarding skins (you should have 1 1/2 cups persimmon puree). Whisk in milk; set aside.
Put butter and sugar into the bowl of an electric mixer fitted with the paddle attachment; mix on medium speed until pale and fluffy. Mix in eggs, vanilla, and lemon juice. Add persimmon mixture in 2 batches, scraping down sides of bowl after each addition. Mix in baking soda mixture. Add flour mixture; mix until just combined. Stir in pecans, sultanas, and ginger. Pour into prepared mold; cover with buttered parchment and lid.
Bring water in prepared pot to a boil; reduce heat to a simmer. Carefully lower mold into steamer. Cover pot, and steam until a cake tester inserted in center comes out clean, 3 to 3 1/2 hours, checking occasionally to make sure water level is maintained (add hot water as needed).
Transfer mold to a wire rack; remove lid and parchment. Let cool 15 minutes. Unmold pudding onto a plate, and cut into slices. Serve with persimmon slices and Calvados cream.