This cake has 3 layers, 2 of which are flavoured with vanilla extract and 1 is flavoured with cocoa powder. In order to save time, you can prepare the the 2 vanilla layers as one cake and cut it afterwards. Below is the recipe for 1 layer only, using 1/3 of the above listed ingredients. Therefore if you will bake the 2 vanilla layers together, you need to double the ingredients.
Preheat oven to 180 degrees C (350 degrees F). Place a circle of baking paper on the bottom of a 23 cm (9 inch) cake pan. Grease well inside the pan.
In a large mixing bowl beat together 90 ml olive oil and 150 g sugar until well combined (mixer is not mandatory, I used a hand whisk). Add 1 egg and whisk well until the mixture thickens.
In a cup combine 180 g yogurt with 1/2 teaspoon baking soda and whisk. When the mixture starts bubbling, add it to the mixing bowl. Whisk until homogeneous.
Gradually add 125 g flour and 80 g ground walnuts and stir until just absorbed. Add the cocoa powder to the cocoa layer or 1 teaspoon vanilla extract to each vanilla layer.
Pour the batter into the cake pan and bake for 30-40 minutes (if baking the 2 vanilla layers as one cake, it would need at least 50-60 minutes). Test with a wooden skewer: if inserted in the centre it comes out just with a few crumbs, the cake is ready.
Let the cake cool about 10 minutes in the pan before taking it out. The layers must be at room temperature before assembling them.
Normally 60 g pudding mix is prepared with 500 ml milk, as per the instructions on the package, but I advise you to use only 450 for a thicker texture.
In a cup combine the vanilla pudding mix with 3 tbs sugar and 30-40 ml milk. Stir until the cornstarch is completely dissolved. Pour the remaining 410-420 ml milk in a medium saucepan and bring it to boil. Once the milk starts simmering, remove from heat and add the pudding mixture. Place the pan on the heat again and whisk continuously until the pudding thickens. Remove from heat and let cool for about 20 minutes before assembling the cake.
Using the same method, prepare the chocolate pudding.
To assemble the cake:
In case you baked the vanilla layers as one cake, use a serrated knife to halve it horizontally. For best results refrigerate the cake in advance.
Place one vanilla layer on a serving plate and cover it generously with warm vanilla pudding. Place the cocoa layer on top and cover it with more vanilla pudding. Place the second vanilla layer on top.
Frost the cake all around with the remaining vanilla pudding.
Spoon the chocolate pudding on top so that it drips around. You will not going to use it all for the cake: the remaining quantity can be distributed in ramequins and consumed directly.
Decorate the cake with ground and whole walnuts.
The pudding used in this recipe is practically flavoured cornstarch or potato starch. Alternatively you can use just plain cornstarch and add cocoa powder and vanilla extract to it.