Preheat oven to 350 degrees F (180 degrees C). Line two 9-inch (23-cm) round cake pans or one 9x13-inch (23 x 33 cm) rectangular baking pan with parchment paper. Grease the paper and the sides of the pan well.
In a large mixing bowl, with an electric mixer, beat sugar and eggs together until slightly thickened, about 1 minute. Add flour, milk, oil, baking powder, and vanilla and beat for another minute, just until the batter is smooth and creamy. Don't overbeat. Pour batter into the prepared baking pan(s).