Preheat the oven to 350ºF (180ºC). Lightly grease an 8-inch (20-cm) round cake tin with oil. Line the bottom of the pan with a circle of parchment paper cut to fit.
Combine the flour, baking powder, baking soda, sugar, cocoa powder, and salt in a large mixing bowl and whisk well.
Add the oil, water, sourdough discard, apple cider vinegar, and vanilla to the bowl. Stir until everything is well mixed and the flour is just combined.
Pour the cake batter into the prepared tin. Place the cake in the oven and bake for 28 to 30 minutes, or until the top of the cake bounces back when lightly pressed with a fingertip.
Transfer the cake to a wire rack to cool in the tin. Once cooled, turn the cake out of the tin and decorate with your favourite frosting.