Preheat the oven to 350 degrees(F).
In a large mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Make sure there are no lumps.
Pour the non-dairy milk, vinegar, oil, applesauce, vanilla and the warm coffee into the bowl. Continue to whisk until fully combined.
Use a spatula to scrape down the sides of the bowl and make sure there are no dry spots of flour left. The mixture will be a bit bubbly and may look a little thin.
Pour the batter evenly into 2, 9-inch cake pans that are lined with parchment paper. Smooth out the batter.
Bake for 30 to 35 minutes or until a toothpick comes out clean from the center.
Let the cake layers cool completely and then frost them with whatever flavor frosting you want. Stack them together to create a two layer cake. Serve.