Preheat the oven to 350°F (175°C). Lightly grease two 8-inch (20 cm) round cake pans and line the bottoms with parchment paper; grease the parchment as well. Set aside.

In a large bowl, whisk together the all-purpose flour, granulated sugar, cocoa powder, baking powder, baking soda, and sea salt until evenly combined and no lumps remain.

In a separate medium bowl or large measuring cup, combine the plant milk and apple cider vinegar; stir and let sit 2 minutes to curdle (vegan 'buttermilk'). Add the applesauce, vegetable oil, vanilla extract, and instant espresso powder (if using). Whisk until smooth.

Pour the wet ingredients into the dry ingredients and stir gently with a spatula or wooden spoon until just combined. Do not overmix; some small lumps are okay.

Add the hot water and stir carefully until the batter is smooth. The batter will be fairly thin — this is normal and helps produce a moist cake.

Divide the batter evenly between the two prepared pans (use a scale or measure visually). Smooth the tops with a spatula. Tap the pans once on the counter to release large air bubbles.

Bake on the middle rack for 25–32 minutes, rotating once halfway through baking, until a toothpick inserted into the center comes out with a few moist crumbs but no wet batter. Oven times vary — watch closely starting at 25 minutes.

Remove cakes from the oven and let cool in the pans on a wire rack for 10–15 minutes. Run a thin knife around the edges, then invert cakes onto the rack, remove parchment, and let cool completely (about 1 hour) before frosting.

Vanilla Frosting

While the cakes cool, make the frosting. In a large mixing bowl, beat the softened vegan butter on medium speed for 1 minute until smooth and slightly whipped.

Sift the powdered sugar into the bowl in two additions, beating on low speed to combine after each addition to avoid a cloud of sugar. After sugar is incorporated, add the soy/almond milk, vanilla extract, and salt.

Increase mixer speed to medium-high and beat for 1–2 minutes until light, smooth, and spreadable. If frosting is too thick, add additional milk 1 teaspoon at a time; if too thin, add 2 tablespoons powdered sugar at a time until desired consistency is reached.

Assembly & Garnish

If cake tops have domed, level them with a serrated knife or cake leveler so layers sit flat. Place one layer on a serving plate or cake board.

Spread about one-third of the frosting evenly over the first layer using an offset spatula, leaving a small margin at the edge. Place the second layer on top, cut-side up (or right-side up for a more uniform top).

Spread a thin crumb coat of frosting over the top and sides. Chill the cake in the refrigerator for 15–20 minutes to set the crumb coat.

Remove the cake from the fridge and apply the remaining frosting evenly over the top and sides. Smooth with an offset spatula or create decorative swirls as desired.

For chocolate shavings: using a vegetable peeler, shave the edge of the chilled dark chocolate bar to create curls/shavings. If chocolate is too hard, microwave for 5–7 seconds to soften slightly (do not melt).

Arrange chocolate shavings on top of the frosted cake, pressing gently so they adhere. Dust lightly with cocoa powder if desired.

Chill the decorated cake for 10–15 minutes to set the frosting, then bring to room temperature 20–30 minutes before slicing for best texture.