The end result will give you a very heavy cake. But it will be moist.

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Milk-free, Egg-free Yellow Cake

2 tsp arrowroot (optional)
1/4 cup brown sugar
3/4 cup white sugar
1 tsp baking powder
1 tsp baking soda
1 1/2 tsp vanilla
1 tsp lemon juice or vinegar
5 Tbsp canola oil
1 cup cold water

Preheat oven to 350. Grease an 8x8 pan.

Mix dry ingredients in a medium bowl. Add liquid ingredients and beat for 2 minutes. Pour into 8x8 pan and bake at 350 for 30-35 minutes or until a knife inserted comes out clean.