With the rack in the middle position, preheat the oven to 180 °C (350 °F). Butter a 20-cm (8-inch) round springform pan. Line bottom with parchment paper.
In a bowl, combine flour, cornstarch, baking powder and baking soda. Set aside.
In another bowl, combine milk and vinegar. Set aside.
In a third bowl, stir condensed milk, brown sugar, butter and vanilla with a whisk. Add dry ingredients alternately with milk mixture until smooth. Pour into prepared pan. Bake for about 55 minutes or until a toothpick inserted in the centre of the cake comes out clean. Let cool on a wire rack before removing from pan.
If you want, remove the rounded top of the cake before frosting it. Cut cake in half horizontally. Spread inside with a third of the Egg-Free Buttercream. Close cake and frost completely with remaining buttercream.