Prepare four 8-inch camp Dutch ovens by spraying with oil, then dusting with a light coat of flour, then adding a round piece of parchment paper that fits in the bottom of the oven.
In a medium mixing bowl, cream together eggs and sugars until smooth. Beat in oil, buttermilk, vanilla, amaretto, and rum. Fold in shredded carrots, pineapple, pecans, and currants.
In a separate bowl, sift together flour, baking soda, salt, nutmeg, and ginger. (Why sift? To completely integrate all of the dry ingredients and to a bit of loft to the cake.) Gently fold into wet ingredients until just combined. It is okay if there are a few small clumps of dry ingredients. The less you stir the batter, the lighter the cake will be.
Pour cake batter into prepared camp Dutch ovens, dividing evenly between the four ovens. Bake cakes at 350 degrees Fahrenheit by placing a circle of 5 hot charcoals underneath each oven and 11 hot charcoals around the lid of the oven. Bake for 15 to 18 minutes or until the top springs back from gentle touch and a toothpick comes out cleanly with just a few crumbs.
Remove all charcoal and let the ovens sit with out the lid for 5 minutes. Place ovens (without lids) into an ice bath with the top of the water coming half way up the side of each oven. Chill cakes completely. Run a table knife around the outer edge of each cake to make sure the cake releases completely. Invert cake on to a wire rack. Remove parchment paper.
While cakes are baking and cooling, prepare frosting. In a large mixing bowl, beat butter and cream cheese together until light and fluffy. Add confectioners’ sugar, orange zest, vanilla, and maple syrup and beat until fluffy. Fold in amaretto and rum. Chill completely before frosting the cake.
Prepare a 12-inch cardboard cake round by cutting two pieces of parchment paper that are long enough to cover the cake round. Overlap one piece on top of the other and center in the middle of the cake round. Place one of the chilled carrot cakes in the center of the cake round. Spread 1/4 cup of the frosting on top of the cake. Repeat. Place the last cake on top and frost top of cake with one cup of frosting. Use remaining frosting to cover the sides. Hold the cake with one hand and gently press the chopped pecans to cover all the sides completely. Chill cake for at least one hour before serving. Remove the parchment paper pieces by carefully sliding them out from underneath the cake. Sprinkle any remaining pecans around the base of the cake.