Preheat your oven to 350F. Butter or spray two 8 x 8-inch square baking pans and line the bottoms with parchment paper. Add the flour, cornstarch, baking soda, baking powder, and salt to a large mixing bowl. Mix to combine.
In a separate mixing bowl, add the non-dairy milk and lemon juice. Allow them to sit for a few minutes. Then, add the sugar, oil or melted vegan butter, and vanilla extract.
Whisk the wet ingredients together until they're mixed.
Pour the wet ingredients into your dry ingredients. Use a spatula to fold everything together. Avoid any streaks of flour, but little clumps in the batter are OK.
Pour the batter as evenly as you can into the two cake pans. Use an inverted spatula to spread the batter; the layer of batter will be thin.
Bake the cakes for 15-20 minutes, or until the cakes are golden brown at the edges and set in the center. Allow the sponge cakes to cool for 10 minutes, then remove the sponges from the pans and allow them to cool for another 30 minutes on cooling racks.