Make the soft base: Using a hand mixer, beat the eggs, sugar, and vanilla extract until light and fluffy. While mixing, slowly add the oil and milk. Then add the flour and baking powder. Pour the batter into a greased and floured 11-inch (28 cm) tart pan. Bake in a conventional oven at 350°F (180°C) for 20–25 minutes. Check doneness with a toothpick, let cool in the pan, then remove from the pan.

Make the pastry cream: Beat the egg yolks with sugar and vanilla extract until the mixture is pale and fluffy. Add the flour and continue beating until smooth. In a separate saucepan, heat the milk with vanilla and lemon zest. Gradually add the hot milk to the egg mixture, then cook over low heat, stirring constantly, until thickened. Let cool.

Once the base is cool, place it on a serving plate. Use a spoon to gently remove the center of the cake and set the crumbs aside. Fill the center with the cooled pastry cream.