With the rack in the middle position, preheat the oven to 180 °C (350 °F). Butter and line the bottom of two 20-cm (8-inch) springform pans with parchment paper.
In a bowl, combine the flour and baking soda. Set aside.
In another bowl, beat the eggs, sugar, oil, vanilla, and vinegar with an electric mixer for 2 to 3 minutes. At low speed, add the dry ingredients alternately with the milk and beat until smooth.
Spoon the batter into the pans. Bake for about 35 minutes for dark pans or 45 minutes for light pans, or until a toothpick inserted in the centre of the cake comes out clean. Let cool. Unmould and let cool completely on a wire rack.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.