Preheat the oven to 350°F or 180°C. Grease and flour (or line) a 8" (20 cm) cake pan, and set aside.
In a glass, mix the cornstarch and 2 tbsp water and set aside.
In a bowl, mix your dry ingredients together (flour, sugar, vanilla sugar, baking soda, baking powder and salt), and set aside.
In another bowl, mix the oil, non-dairy milk and cornstarch mixture together until combined.
Add the wet ingredient mixture to the dry ingredient mixture, and mix everything until incorporated.
Place the batter in the cake pan.
Bake for 15-20 minutes, or until you insert a toothpick and it comes out clean or with a few crumbs.
Allow to cool completely (about 1-2 hours).