Make the syrup by combining the ingredients for it and bringing it to boiling point.
In a bowl, put the sugar, add the yoghurt and baking soda, stir well with a whisk. To these, add the oil, cocoa and stir again. Add the sifted flour cup by cup, while stirring nonstop.
Pour the mixture into an oiled oven dish and bake at 356°F (180 °C) until ready, checking to see with a toothpick if it is.
Poke holes in the cake with the tip of a sharp knife and pour the cold syrup over the hot cake. Leave to cool completely. In the meantime, make the cream by beating the soft butter with the powdered sugar and vanilla.
My grandma used to do this with a whisk, which took her quite a lot of time but I just do it with a mixer until I get a fluffy buttercream.
Smear the cooled cake with the cream and sprinkle with ground walnuts.