In a medium saucepan, whisk together the egg, a pinch of salt, and sugar until well combined.

Add the cornstarch and mix until smooth.

Gradually pour in the milk, stirring continuously to avoid lumps.

Place the saucepan over medium heat and add the grated lemon peel and lemon juice.

Cook, stirring constantly, until the mixture thickens to a pudding-like consistency. This should take about 5-7 minutes.

Once thickened, remove from heat and set aside to cool.

Preheat your oven to 190°C (370°F) and grease a 23 cm (9-inch) baking pan.

In a large mixing bowl, beat the eggs, a pinch of salt, and sugar until the mixture is light and fluffy.

Add the vegetable oil and vanilla extract, mixing well to combine.

Gradually add the flour and baking powder, folding the dry ingredients into the wet mixture until just combined. If the batter is too thick, add a little milk and mix until smooth.

Pour half of the batter into the prepared baking pan, spreading it evenly.

Bake in the preheated oven for 15 minutes.

Remove the partially baked cake from the oven and carefully spread the cooled lemon pudding over the top.

Pour the remaining batter over the pudding layer, spreading it evenly to cover.

Return the cake to the oven and bake for an additional 30 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.