Place raisins in a microwave-safe bowl and drizzle with the 3 tbsp of orange liqueur; cover with plastic wrap or a lid and microwave on Medium power for 1 or 2 minutes, until the raisins are warm; remove from microwave and set aside.
Preheat oven to 350F; lightly butter or spray with non-stick cooking spray three 9-inch round cake pans or three of the disposable 8 1/2-inch or 9-inch foil pans.
Line the bottom of each pan with a circle of parchment paper or wax paper, lightly greased; set pans aside.
Scrape carrots and grate, using either the grating disc in your cuisinart or on the large holes of a box grater; you do NOT want to grind the carrots, you want them shredded.
Grated carrots should measure out to be 3 1/2 cups; don't use any more than that or your cake's texture will definitely suffer.
In a mixing bowl, with electric mixer, beat together eggs, orange zest, brown sugar, oil and vanilla; beat until smooth.
In another mixing bowl, combine flour, baking powder, baking soda and spices; I do this by sifting all through a sieve into the bowl.
Make a well in the centre of the dry mixture and pour in egg mixture, stirring just until moist.
Carefully fold in carrots and raisins (and any remaining liqueur).
Divide evenly among three prepared pans; smooth tops.
Bake in preheated oven until a tester comes out clean when inserted in centre of cakes, 25 to 30 minutes.
When done, remove cakes from oven and cool in pans for 10 minutes, then turn out onto a rack and let cool thoroughly.
You could now wrap the cakes tightly and refrigerate them overnight, if you wanted to ice the cake the next day.
To make the icing, beat softened cream cheese (2 250 gram or 8 oz bars= one pound) in a large mixing bowl with electric mixer until creamy.
Beat in icing sugar, vanilla and liqueur, combining well.
Place one layer of cake on a plate and spread one-third of icing over cake layer, going right to the edges.
Repeat with the next two layers.
If desired, sprinkle the toasted coconut over the top layer of icing.
Refrigerate cake for at least one hour before serving, and keep leftover cake in the fridge, well covered.