Stir flour, 1 1/2 cups sugar, cocoa powder, baking soda, and salt together in a 8x12-inch baking pan. Make 3 wells in the mixture. Pour oil, vinegar, and vanilla extract each into their own well. Pour water into the pan. Stir batter with a fork until well combined.
Combine 1/3 cup sugar and cinnamon in a bowl. Sprinkle 3/4 of the mixture over the batter.
Bake in the preheated oven until a toothpick inserted in the center comes out clean, 30 to 40 minutes. Sprinkle the remaining cinnamon sugar over the hot cake. Let cool before slicing, at least 15 minutes.