Position a rack in the center of the oven and preheat to 350°F. Lightly grease an 9x13 pan.
Sift the flour, cocoa, baking soda, and salt directly into the baking pan, then add the sugar. With your finger, poke 2 small holes and 1 large one in the dry ingredients. Into one of the small holes pour the vanilla, into the other one the vinegar, and into the larger one the oil.
Pour the water over all the ingredients and stir the ingredients together with a table fork, reaching into the corners, until you can’t see any more flour and the batter looks fairly well homogenized.
Bake for 35 to 40 minutes, or until the top is springy and a tester inserted in the center comes out dry. Cool the cake in the pan on a wire rack, then cut and serve it from the pan.
Notes
315 calories per piece, including frosting
Substitute flour for the coco powder for a vanilla cake.