Preheat the oven to 350°F. Brush 2 8" or 9" round spring-form pans** with melted coconut oil. Line the bottom with parchment paper and brush the parchment with oil.
In a large mixing bowl, combine flour, cocoa powder, baking soda and salt. Whisk well to combine.
In a medium mixing bowl, whisk together the nondairy milk and vinegar vigorously until frothy. Whisk in the sugar, oil and vanilla.
Add about ⅓rd of the wet ingredients to the dry ingredients and stir until combined. Repeat adding the remaining wet ingredients in two more additions, mixing just until incorporated after the final addition.
Pour the batter into the prepared pans.
Bake for about 25 minutes or until a toothpick inserted into the center comes out clean. Remove from the oven but leave the cakes in the pan until completely cooled.