Preheat the oven to 350° (175°C). Slightly grease three 6-inch cake pans and line them with parchment paper.
In a large mixing bowl, whisk together the flour, coconut sugar, unsweetened cacao powder, baking powder, baking soda, and salt. Add the vegan yogurt, oil, applesauce, and almond milk. Whisk until the batter is smooth.
Next, add the brewed coffee and vanilla extract and whisk until fully combined.
Divide the batter evenly between the three cake pans. Bake for about 20 minutes, or until the cakes have just slightly cracked tops. You can test doneness by inserting a toothpick inside the cake. It should come out clean. Note: Do not overbake. You want to keep the cakes moist and tender.
Remove from the oven and let the cakes cool for at least 30 minutes before carefully flipping over a cooling rack. Let cool completely at room temperature before frosting.
Chocolate Frosting
Cream the butter using a hand or a stand mixer for about 1 minute. Once the butter appears fluffy, add the powdered sugar, cacao powder, almond milk, vanilla extract, and salt.
Beat on low speed for another 30-40 seconds or until fully combined. If the frosting appears too soft, you can add more cacao powder/powdered sugar. If it seems too thick, add an extra tablespoon of almond milk.
Assembling
Place one chocolate cake on a cake stand or flat plate. Cover the top with a generous amount of chocolate frosting, then carefully top with the second chocolate cake and repeat. Finish by placing the last chocolate cake on top of the second one. Frost the top and sides, and smooth using a spatula. Note: you might have frosting leftover. Use it for muffins or cupcakes!
Refrigerate the frosted cake for about 1 hour before serving to allow the frosting to firm up a bit.
This cake is best served the same day but will keep for up to 5 days in the refrigerator.