For the cake:
Preheat oven to 350°F.
Spray 3 (9-inch or 6-inch) round cake pans with baking spray with flour.
Line bottom of pans with parchment paper, and spray pans again.In a large bowl, stir together flour, sugar, candied orange peel, candied ginger, freeze dried pineapple, gingerbread spice, baking soda, baking powder, and salt.
Add carrot, pineapple, oranges, eggs, oil, and vanilla, stirring until well combined.
Divide batter among prepared pans.
Bake until a wooden pick inserted in center comes out clean, about 25 minutes if using 9-inch rounds. About 40 minutes for 6-inch cake rounds.
Let cool in pans for 10 minutes.
Remove from pans, and let cool completely on wire racks.
For the Buttercream:
Place the egg whites and sugar in the metal bowl of a stand mixer and set over a small pot of simmering water (the bowl should not touch the water).
Heat, stirring occasionally, until mixture is 160F or hot to the touch.
Transfer bowl to stand mixer and beat on high speed with a whisk attachment to medium stiff peaks, about 8 minutes.
Reduce mixer speed to medium low and add butter a tablespoon at a time, letting it incorporate into the meringue for few moments before adding more.
Add vanilla extract, 1 cup orange marmalade, and salt and beat on high for 1-2 minutes until smooth and creamy.
Place a cake layer on cake plate and pipe 3/4 cup of buttercream.
Spread a 1/3 cup orange marmalade on top of the frosted layer.
Place second layer on top of the orange marmalade and push down slightly until you see the marmalade come to the sides.
Pipe another 3/4 cup of the buttercream followed by the remaining orange marmalade.
Top with the last cake layer.
Frost the cake with a crumb coat layer and let set up for 30 minutes in fridge.
Remove from fridge and frost the cake.
Garnish with candied orange peel if desired.