Chop the nuts finely. Peel and grate carrots. Put flour, baking powder, sugar, vanillin sugar, salt and cinnamon in a mixing bowl and mix well. Stir in oil. Stir in the eggs one by one. Add carrots and nuts to the dough
Pour the dough into a greased springform pan (20 cm Ø) sprinkled with flour and smooth it down. Bake in a preheated oven (electric cooker: 175 °C/ convection oven: 150 °C/ gas: see manufacturer) for 1 1/4-1 1/2 hours. Cover the cake with aluminium foil about 40 minutes before the end of the baking time. Remove from the oven, place on a cake rack, remove from the edge of the springform pan and allow to cool. Then remove from the tin
Select the blueberries, wash and drain well. Wash lime hot, grate dry, grate peel thinly, halve fruit and squeeze juice. Mix cream cheese and cream with the whisk of the hand mixer until smooth. Add icing sugar and whisk until thick and creamy. Stir in lime zest and juice
Cut the cake 2 x horizontally. Remove 1/3 of the cream, cut in half. Spread one half on the bottom cake base. Spread about 1/3 blueberries on the cream and press in. Place the middle cake layer on the cream and continue with the other half of the cream, blueberries and the upper cake layer. Spread the rest of the cream on the cake. Sprinkle with the remaining blueberries and brown sugar. Stir the spread and apple juice until smooth and pour over the berries
Waiting time approx. 1 hour