With the rack in the middle position, preheat the oven to 350 °F (180 °C). Butter two 8-inch (20-cm) springform 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 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. If necessary, cut and remove the cake tops to level each cake before frosting.