Preheat oven to 350ºF. Lightly grease two 8-inch round cake pans with coconut oil. Dust with cocoa powder. Shake out the excess and set aside.
Whisk together the non-dairy milk and vinegar in a large mixing bowl. Set aside for a few minutes to curdle. Add melted coconut oil, instant coffee, vanilla, and applesauce. Whisk to combine.
In a small bowl, whisk together flour, sugar, cocoa powder, baking soda, baking powder, and salt. Pour over the wet ingredients and stir to combine, being careful not to over mix. Divide batter evenly between two cake pans.
Bake 25 to 30 minutes, or until a toothpick inserted into the center comes out clean. Let cool completely before frosting.
To make the frosting, use an electric mixer to beat the vegan butter till light and creamy. Sift powdered sugar into bowl, 1 cup at a time, and beat again. Add vanilla. Add non-dairy milk, one tablespoon at a time, until desired consistency is achieved. If it becomes to thin, add more sifted powdered sugar.
Invert cake pans to remove cake. Spread a dab of frosting onto the cake plate. Place one layer of cake topside down onto the dab of frosting, which will keep it from sliding. Add a few heaping spoons of frosting onto the first layer. Spread then sprinkle a couple of tablespoons of Oreo crumbs. Invert the second cake layer, and place on top of the first. Scoop put remaining frosting and spread evenly over top and then down the sides. Sprinkle more Oreo crumbs on the top and press into the sides of the cake. Garnish with Oreo cookies around the perimeter of the cake. Slice and serve.