Grease a 10-inch (25-cm) springform pan.
Preheat oven to 375°F (190°C).
To make cake, put 7 egg yolks, sugar, salt, cinnamon, cloves and kirsch into a large bowl.
Beat until thick and creamy, 5 to 10 minutes with an electric mixer.
Sift flour with baking powder into a medium bowl.
Mix in carrots, almonds, hazelnuts and breadcrumbs.
Stir carrot mixture into egg yolk mixture.
Beat egg whites until stiff; fold into egg yolk and carrot mixture.
Turn cake batter into greased pan; smooth the surface.
Bake 45 to 55 minutes or until a wooden pick inserted in center comes out clean.
Turn out cake onto a rack to cool.
Cover cooled cake and let stand 2 days.
To make frosting, combine powdered sugar, kirsch and lemon juice in a small bowl.
Spread frosting over top of cake.
To decorate cake, warm jam and spread over sides of cake.
Press on sliced almonds.
Knead orange food coloring into almond paste and shape into small carrots.
Insert a couple of pistachio nut pieces into top of each carrot to resemble stem.
Arrange carrots on top of cake.