Preheat the oven to 350 degrees F. Grease two 8-inch-round cake pans and line each bottom with a round of parchment paper.
Beat the sugar and eggs together until smooth and pale. Slowly beat in the oil, scraping the sides of the bowl so it is evenly blended. Sift together the flour, baking soda, cardamom, cinnamon, fennel, nutmeg, cloves and salt and add to the eggs. Continue to beat until it is just combined. Stir in the carrots and coconut and pour the batter into the prepared pans. Bake until the cake is firm to the touch and a toothpick inserted into the center comes out clean, 35 to 40 minutes. Let cool and remove the cakes to a cooling rack. Cool completely before frosting.
To frost: Place a cake layer on a cake platter and cover with a layer of the Spiced Mascarpone Frosting. Place the second layer on top of it and frost the rest of the cake. Scatter the toasted coconut on top.
Beat the cream cheese, mascarpone and butter together until smooth and creamy. Add the icing sugar, lemon juice, cardamom, cloves and salt and beat until light and fluffy. If the icing seems a little runny, add a little more icing sugar until it reaches the desired consistency. Use immediately for frosting the cake. Freeze any unused frosting for another use.