Make the cake: Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Brush three 9-inch-round cake pans with vegetable oil and line the bottoms with parchment paper. Spread the pecans on a baking sheet and bake until toasted, about 10 minutes. Let cool, then pulse in a food processor until very finely chopped.
Combine the pecans, flour, baking powder, baking soda, salt, cinnamon, ginger and granulated sugar in a large bowl. In another bowl, whisk the vegetable oil, lemon zest, eggs and 1/2 cup marmalade. Stir in the carrots, then fold the carrot mixture into the flour mixture until just combined. Divide among the prepared pans and spread evenly (it won't look like a lot of batter, but the cakes will rise in the oven). Put 2 pans on the upper oven rack and the third pan on the lower rack. Bake until the cakes bounce back when touched and a toothpick comes out clean, 20 to 25 minutes, switching the position of the pans halfway through. Transfer the pans to racks until cool enough to handle, then invert the cakes onto the racks to cool completely. Remove the parchment.
Make the frosting: Beat the cream cheese and butter in a bowl with a mixer until smooth, scraping down the bowl as needed. Beat in the confectioners' sugar, lemon juice, vanilla and salt until smooth.
Put 1 cake layer on a platter. Spread with 1 tablespoon marmalade, then spread about 3/4 cup frosting over the marmalade. Top with another cake layer, marmalade and frosting. Spread the final cake layer with a thin layer of frosting. (This is the crumb coat; it doesn't have to be perfect.) Refrigerate 1 hour, then cover with the remaining frosting. Swirl some marmalade into the top of the cake. Refrigerate until ready to serve.
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