Grease a fat pan (deep baking tray; approx. 32 x 39 cm) and dust with flour. Preheat oven (electric cooker: 150 °C/circulating air: 125 °C/gas: see manufacturer). Whisk eggs, 300 g sugar and vanilla sugar for about 5 minutes until thick and creamy.
Mix 350 g flour and baking powder, stir in briefly. Also briefly stir in oil and lemonade. Pour the dough onto the fat pan and spread evenly. Bake in a hot oven for 25-30 minutes. Remove from the oven and let cool on a cake rack.
Stir mascarpone with 250 g sugar, cream firming agent, lemon peel and juice until smooth. Whip cream in 2 portions until stiff, fold into the mascarpone one after the other. Pour the cream onto the base and smooth it down.
Cut the cake into squares of about 6 x 6 cm and chill until serving. Decorate each piece with lemon wedges and straws if desired.