Preheat the oven (electric cooker: 175 °C/recirculating air: 150 °C/gas: see manufacturer). Coat an ovenproof dish (approx. 20 x 20 cm; approx. 5 cm high) with oil. Wash lemon hot, dry and finely grate peel.
Squeeze the lemon. Mix flour, sugar, vanilla sugar, baking powder, 1 pinch of salt and lemon peel. Distribute in the form.
Press 2 small wells and 1 somewhat larger well into the flour mixture. Add vinegar, 4 tablespoons lemon juice and 100 ml oil to each well. 1⁄2 Pour l cold water over the whole flour mixture. Mix to a smooth dough with a dough scraper or wooden spoon.
Bake in a hot oven for about 45 minutes.
Take out the cake. Sprinkle with lemon icing while still slightly warm or dust with icing sugar as desired. Let it cool down.