Preheat the oven to 350° F.
Spray a 8 x 8 inch baking dish with cooking spray and set aside.
In a small bowl, mix the powdered egg substitute to the package directions.
Measure the plant based milk into a measuring cup.
Stir in the apple cider vinegar, and set aside to curdle, this is the vegan buttermilk.
Next, mix together the oat flour, baking powder, baking soda, and ground cinnamon in a medium sized mixing bowl.
Peel and shred the carrots, place into the flour mixture.
Continue by adding the egg substitute, vegan buttermilk, vanilla, maple syrup, and mashed banana.
Combine until there are no lumps, then fold in the raisins and nuts if you are adding any.
Spread the batter into the prepared baking dish.
Place into the oven and bake for 45 minutes.
After 45 minutes, test the cake with a toothpick to see if the cake is done, if not, place back into the oven for another 10 to 15 minutes.
Once the cake is done, remove from the oven to cool completely before adding a glaze or frosting.