Preheat the oven to 180 °C (350 °F). Butter two 20-cm (8-inch) spring form pans and line the bottom with parchment paper. Set aside.
In a bowl, combine the flour, baking powder, and salt. Set aside.
In another bowl, beat the eggs, sugar, and vanilla with an electric mixer for about 10 minutes or until thick, pale and triple in volume. Drizzle in the oil while beating.
At low speed, add the dry ingredients alternately with the milk until the batter is smooth. Divide the batter into the pans and bake for 50 to 55 minutes or until a toothpick inserted in the centre of the cake comes out clean. Let cool for 15 minutes. Remove from the pans and let completely cool on a wire rack.
Leave the ice cream at room temperature for at least 30 minutes.
Cut each cake into 3/4 to 1/4 proportions. In the same baking molds, cover with saran wrap, then place the 3/4 portion of the cake on top of it add the vanilla ice cream then top with the 1/4 portion of the cake. Do the same with the other cake and the chocolate ice cream, put in the freezer over night.
Remove both cakes from the molds, cover with butter cream frosting or Italian meringue, and serve right away!