Preheat oven to 350°F and spray a 9x13 cake pan with vegetable spray.
In a large bowl, combine the flours, sugar, cocoa, baking powder, baking soda, salt, cloves, and nutmeg. Stir until well combined.
Create a well in the middle of the flour and pour in the plant-based milk, chai tea, ground flax seeds, corn starch, apple cider vinegar, and oil. Stir to combine. Slowly incorporate the flour mixture into the milk mixture and continue stirring until well-combined.
Pour the batter into the prepared pan and bake for 35 to 40 minutes until a toothpick inserted in the middle comes out clean. When the cake is done, remove from the oven and set aside to cool completely before frosting.
While you're waiting for the cake to cool, prepare the frosting by combining the softened vegan butter, cocoa powder, and powdered sugar in a bowl. Stir to combine. It should form a thick mixture. Add the vanilla and one tablespoon of plant-based milk at a time until you reach a desired, spreadable consistency. Spread this evenly across the top of the cooled cake.
Cover the cake and store at room temperature for up to 3 days, in the fridge for up to 7 days, or cut individual slices and freeze them for up to 2 months. To serve, cook individual slices in the microwave in 10 to 15-second intervals until warmed through.