Grease a box cake tin (25 cm long; 1 1⁄2 l capacity) well and dust with flour. Cut the avocado in half lengthwise and remove the core. Remove the flesh from the skin. Pour lemon juice into a tall mixing bowl.
Puree finely with a hand blender.
Preheat oven (electric cooker: 175 °C/circulating air: 150 °C/gas: see manufacturer). Cream 225 g butter, sugar, vanilla sugar and 1 pinch of salt with the whisks of the mixer. Stir in eggs one after the other.
Mix 350 g flour, baking powder and almonds. Alternately stir in flour mix, avocado puree and milk.
Fill the dough into the box form, smooth it down. Bake in a hot oven for 60-70 minutes (test with wooden sticks). About 20 minutes before the end of the baking time cover the cake with aluminium foil. Remove from the oven and let it cool down on a cake rack for about 40 minutes.
Then carefully fall out of the mould. Let it cool down.
Coarsely chop the pistachios. For the icing, stir icing sugar and lime juice until smooth, stir in lime zest. Cover the cake with the icing. Sprinkle with pistachios and let dry.