I took a cooking class recently from Marcella Hazan's son, Giuliano Hazan. This was the dessert we made in class. It's the best carrot cake I've ever had and contains no flour. It keeps well in the refrigerator for a week!
Put the almonds and sugar in a food processor and chop as finely as possible. Transfer to a large mixing bowl. Break up the ladyfingers into pieces, about an inch long, place them in the food processor and grind to a powder. Add to the almonds and sugar in the mixing bowl. Cut the carrots into pieces about an inch long, and chop in the food processor as finely as possible. Add to the bowl, mixing them well with the other ingredients.
Add the baking powder, salt, and the Amaretto liqueur and mix well. Add the egg yolks, mixing them in until they are well distributed with the other ingredients.
Whip the egg whites with an electric mixer or by hand until they form stiff peaks. Take a couple of tablespoons of the beaten egg whites and mix them with the ingredients in the bowl to soften the mixture a bit. Pour the rest of the egg whites onto the mixture and carefully fold them in with a rubber spatula.
Grease the bottom and sides of a 10 inch springform pan with the butter and dust it with flour. Pour the batter into the pan, then shake the pan a bit until the batter is evenly distributed.
Place the pan in the upper level of the preheated oven and bake for 50-60 minutes, or until a toothpick comes out dry when inserted into the cake.
When the cake is cool, cut it into 8 to 12 pieces and serve with a dollop of whipped cream.