Preheat oven to 350 F. Spray an 8x8-inch baking pan with non-stick cooking spray; set aside. In a large mixing bowl, whisk together the flour, sugar, baking soda, baking powder, and salt.
Use a spoon to form wells in different areas around the surface of the dry ingredient mixture; two large wells and two small. This is meant to keep the wet ingredients separate until the water is added.
Scoop the pumpkin into one of the large wells. Pour the vegetable oil into the other large well, then the vinegar and vanilla separately into the two small wells. Then pour the water into the bowl and mix until well combined.
Pour the batter into the prepared baking pan. Bake the cake at 350 F for 35-45 minutes, until a toothpick inserted into the center comes out clean....or middle touched gently springs back.
Cool the cake completely on a cooling rack to room temperature then top with the frosting of your choice.