First, make the pudding. Heat the milk with the vanilla and sugar in a casserole. Stir the contents of vanilla packet with 5 tbsp water, pour this in a thin trickle to the milk and stir until thickened. Transfer to a bowl and leave to cool.
In another bowl, beat the eggs with the sugar to fluffy cream. I used a whisk. Pour in the milk and oil. Add the grated lemon rind, stir well. Mix together the flour and baking powder, then sift them through a sieve into the egg mixture.
Stir to a smooth cake batter. Pour the batter into a rectangular tray with baking paper. Pour the cooled pudding into a pastry bag (without any special tip) and pour it out into a grid pattern on the batter (see photos).
Bake in a preheated 356°F (180 °C) oven about 30-35 min. or to a dry toothpick. Take it out onto a cooking grid and sprinkle powdered sugar. Cut into squares with a wavy knife and serve. It's so tasty that you'll be licking your fingers.
I actually cut it right away - the pudding hadn't hardened yet but it tastes excellent this way too. My measuring cup was the glass with the lemons in the picture, so you get an idea.