Preheat your oven to 350°F (175°C). Grease and flour a cake pan.
In a mixing bowl, whisk together the flour, sugar, baking powder, and baking soda.
In a separate bowl, combine the non-dairy milk, vegetable oil, and vanilla extract.
Gradually add the wet ingredients to the dry ingredients, stirring well to form a smooth batter. Ensure there are no lumps.
Pour the batter into the prepared cake pan, spreading it evenly.
Bake in the preheated oven for 25-30 minutes or until a toothpick inserted into the center comes out clean.
Once baked, remove the cake from the oven and let it cool in the pan for 10 minutes. Then transfer it to a cooling rack to cool completely.
Frost or decorate the cake as desired, or simply dust it with powdered sugar.
Slice and enjoy your delicious eggless vanilla cake!