Preheat the oven to 350 degrees F. Butter three 9-inch cake pans with 1 tablespoon butter. Set aside.

In a small saucepan, combine the currants and brandy, if using, and heat until the brandy comes to a boil. Cover, remove from the heat, and allow the currants to "plump" until they've absorbed the brandy, 15 to 20 minutes.

Put the grated carrots in a medium bowl. Melt the remaining 3/4 pound butter in a small saucepan and pour over the grated carrots. Stir to combine well and set aside.

Sift the flour, sugar, baking soda, cinnamon, salt, and nutmeg into a large mixing bowl. Add the eggs, one at a time, beating thoroughly after each addition. Add the vanilla, plumped currants, and the carrot-butter mixture and beat until thoroughly combined. Add the chopped nuts and crystallized ginger, if using, and stir to combine. Divide the batter evenly among the three prepared pans, and bake until a cake tester inserted in the center of each cake layer comes out clean, 22 to 25 minutes. Remove the cakes from the oven and allow to cool in the pans on a wire rack for 5 to 10 minutes before turning out onto a rack to cool. When the cakes have cooled completely, frost as directed below.

Meanwhile, make the icing by creaming the cream cheese and butter until smooth and fluffy, 2 to 3 minutes. Add the sugar and vanilla and mix on low speed until combined. Beat on high speed until the icing is smooth and creamy. Fold in the pecans.

When the cakes have cooled completely, place 1 layer on a cake plate and top with one-third of the frosting. Smooth the frosting to the edges of the top of the cake layer and then top with another layer. Repeat with another third of the frosting and smooth to the edges as before. Top with the remaining layer and finish frosting the top of the cake with the remaining frosting.

Serve immediately or refrigerate, wrapped in plastic wrap, until ready to serve, up to 2 days ahead.