Adjust oven rack to middle position and heat oven to 350 degrees. Coat 8-inch-square baking pan with nonstick cooking spray.
Whisk flour, sugar, cocoa, baking soda, and salt together in pan. Make 1 large and 2 small craters in dry ingredients. Add oil to large crater and vinegar and vanilla separately to remaining small craters. Pour water into pan and mix until just a few streaks of flour remain. Use a rubber spatula to spread the batter evenly in the pan if it isn’t level after mixing. Immediately put pan in oven.
Bake until toothpick inserted in center of cake comes out with a few moist crumbs attached, about 23-25 minutes. Don’t overbake or the cake will be dry! Cool the cake in pan, then dust with confectioners’ sugar. The cooled cake can be stored tightly covered in plastic wrap for 2-3 days. As a sidenote, this cake is made completely otherworldly by serving it with a scoop of ice cream or a hefty dollop of sweetened whipped cream.
For cupcakes, I use the following amounts (after a lot of trial and error): 3 cups flour, 1 3/4 cups sugar, 1/2 cup cocoa, 2 teaspoons soda, 1 teaspoon salt, 3/4 cup oil, 1 tablespoon white vinegar, 2 teaspoons vanilla and 2 cups cold water. Follow the mixing directions, using a bowl instead of a baking pan. Spoon the batter into lined cupcake pans about 1/2 to 2/3 full and bake at 350 degrees for 16-19 minutes.