Preheat the oven to 350°F (175°C). Lightly coat three 8-inch cake pans with nonstick spray and line the bases with parchment paper. (Refer to notes if making a two-layer cake.)
In a small bowl, combine the non-dairy milk with vinegar. Stir and let sit for a few minutes to create a vegan buttermilk.
In a separate bowl, whisk together the flour, sifted cocoa powder, baking powder, baking soda, and salt. Set aside.
In a large mixing bowl, whisk or use a mixer to blend together granulated sugar, applesauce, oil, and vanilla extract until smooth and glossy.
In a small cup, dissolve the instant espresso powder into the hot water and keep aside.
Alternately incorporate the dry ingredients and the prepared buttermilk into the sugar mixture, beginning and ending with the dry mix. Pause halfway to scrape down the sides of the bowl for an even blend.
Once the batter is smooth, gradually pour in the hot espresso mixture and blend until fully combined. The batter will appear quite thin — this is ideal for a moist, tender crumb.
Divide the batter evenly among the prepared pans and bake for 30–35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cakes cool in their pans for 20 minutes. Carefully remove them and place on wire racks to cool completely. For quicker cooling, refrigerate the layers until thoroughly chilled.