Preheat oven to 350 degrees F (or 177 degrees C).
Line two 9-inch round pans with parchment paper. Grease paper and sides of the pans. Put to the side.
In a large mixing bowl, with an electric mixer, beat sugar and applesauce until slightly thickened, approximately 1 minute.
Add flour, soymilk, oil, baking powder, and vanilla extract, and beat for another minute, until batter is smooth and creamy. Don't over beat.
Pour batter into the pans. Bake 30 to 40 minutes or until tops are golden brown and you can stick a toothpick in the center and it comes out clean.

2 cup (16 ounce) sugar
1 cup (8 fl ounce) applesauce, equivalent to 4 eggs
2-1/2 cup (20 ounce) all purpose flour
1 cup (8 fl ounce) soymilk or another non-dairy milk of choice
3/4 cup (6 fl ounce) baking oil, like safflower or sunflower oil
2-1/4 teaspoon (.375 ounce) baking powder
1 teaspoon (.17 fl ounce) vanilla extract