Preheat your oven to 350F. Grease two 8-inch cake pans and set them aside.
In a bowl, mix the milk and vinegar together and let it sit to curdle.
In a large bowl, combine oat flour, cocoa powder, arrowroot powder, baking soda, and baking powder. In another bowl, whisk together the milk mixture, brown sugar, and applesauce. Mix the wet ingredients with the dry ingredients until well combined. Stir in the shredded zucchini.
Divide the batter evenly between the two cake pans. Bake for 35-40 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool completely once out of the oven. Once cooled, frost, layer, slice, and enjoy!