Preheat the oven to 325 (F).
Put the flour, sugar, cocoa, and baking soda in a large bowl and mix with a handheld electruc whisk on slow speed until all the dry ingredients are well incorporated.
Put the oil, vinegar, vanilla, and 1/2 cup water in a glass and whisk to combine.
While the electric whisk is running in the flour bowl, slowly add the oil mixture, increasing the speed of the blender as the mixture thickens. Continue to beat until all the ingredients are incorporated, scraping any unmixed ingredients from the side of the bowl with a rubber spatula.
Spoon the batter into a cupcake pan lined with paper cases and set aside.