In a saucepan, whisk together 1 egg, 50 g sugar, 10 g vanilla sugar, and 15 g cornstarch.

Gradually add 250 ml milk while whisking continuously to prevent lumps.

Cook over low heat, stirring constantly, until the mixture thickens.

Remove from heat and let it cool to room temperature.

Preheat your oven to 170°C (340°F).

In a mixing bowl, beat 2 eggs, 100 g sugar, a pinch of salt, and 1 teaspoon vanilla essence until fluffy and light in color, about 3-4 minutes.

Add 100 ml milk and 50 ml vegetable oil, and mix until combined.

Sift together 220 g flour and 1 teaspoon baking powder, then gradually fold into the egg mixture until just combined.

Line a 27 x 18 cm mold with baking paper.

Pour half of the cake batter into the prepared pan.

Place the cooled pudding into a piping bag and pipe it evenly over the batter in the pan.

Arrange the sliced apples over the pudding layer.

Pour the remaining cake batter over the apples.

Bake in the preheated oven at 170°C (340°F) for 40-45 minutes, or until a toothpick inserted into the center comes out clean.

Allow the cake to cool in the pan for 10 minutes, then transfer it to a wire rack to cool completely.

Once cooled, dust the cake with powdered sugar before serving.