Put all the dry ingredients (flour, baking powder, baking soda, spices, salt) in the bowl, mix: 30 sec. speed. 4 and set aside.
In the empty bowl, place the carrots and nuts, chop: 30 sec. speed. 7 and set aside.
Now in the empty bowl, combine the eggs, sugar, oil and vanilla, emulsify: 1 min. speed 4.
Add the reserved dry ingredients and mix: 1 min. speed 3.
Finally, add the carrot and nut mixture, stir in: 1 min. speed. 4.
Divide the resulting mixture into 3 parts* and pour it into 3 baking sheets (diameter 22 cm).
Bake each tray in a preheated oven at 180°C for about 30 minutes (always do the toothpick test) and let it cool completely.
Take the butter out of the fridge at least 20 minutes first and then put it in small pieces in the mug, whip up: 1 min. speed 4.
Add the cold cheese, whisk again: 1 min. speed. 4.
Add the vanilla extract and a pinch of salt, mix: 10 min. speed 4.
Then, with the blades moving at speed. 3, add the icing sugar a little at a time and whisk for another 2 minutes or until the mixture is smooth and creamy.
Refrigerate in a bowl covered with plastic wrap for at least 15-20 minutes before use (can be kept for up to 6 days in the refrigerator).
Take back the cooled cake discs, fill each one with the cheese frosting and cover the surface of the cake with the leftover one.
If desired, decorate the surface of the cake with chopped nuts.
Refrigerate for at least 1 hour. And before serving it, take it out half an hour... Buon appetito!
*Or you can choose to bake the cake in a single mold for minutes and once completely cooled, cut it into 3 equal discs.
As an alternative to butter and Philadelphia frosting, you can opt for ricotta or mascarpone frosting.