Preheat oven to 350°F and grease an 8×8-inch baking dish with nonstick spray.
In the baking dish, mix together the flour, sugar, brown sugar, cinnamon, baking soda, cream of tartar, and salt.
Make three depressions or wells in the dry ingredients, two small, and one large. Add the vinegar in one small well, vanilla in the other, and vegetable oil in the large one. Pour 1 cup water over the top and mix until smooth.
Bake until a toothpick inserted into the center comes out clean, about 35 minutes.
While the cake bakes, stir together the cinnamon and sugar for the topping. While cake is still hot, sprinkle with cinnamon sugar. Let cool, slice, and serve. Enjoy!