Finely grate the carrots and set aside. Peel the apples, remove the core and cut them into small pieces. Beat the eggs with the sugar and a pinch of salt for at least five minutes, until a light and fluffy mixture is obtained, then add the oil in a steady stream while continuing to work. Add the sifted flour with the yeast and the chopped almonds, alternating them with the grated carrots and the lemon zest, mixing from the bottom up to prevent the mixture from separating. Finally, add the apple pieces, lightly dusted with flour so that they remain suspended and do not fall to the bottom of the pan. Pour the mixture into a 22 cm cake pan lined with baking paper and bake in a preheated static oven at 180°C for about 45 minutes: the cake is ready when a toothpick inserted in the center comes out dry. Leave to cool completely before dusting with icing sugar.