Preheat your oven to 350°F (175°C). Lightly grease two 9-inch round cake pans with vegetable oil or butter, then dust them with cocoa powder to prevent sticking. Set aside.
In a large bowl, sift together the all-purpose flour, granulated sugar, cocoa powder, baking powder, baking soda, and salt. Whisk until well combined.
In a separate bowl, whisk the eggs. Add the whole milk, vegetable oil, and vanilla extract, mixing until smooth. Gradually stir in the hot brewed espresso.
Slowly add the wet ingredients into the dry ingredients, stirring gently with a spatula or wooden spoon until just combined. Avoid overmixing.
Divide the batter evenly between the prepared pans. Bake for 30 to 35 minutes, or until a toothpick inserted in the center comes out clean. Allow the cakes to cool in the pans for 10 minutes, then transfer to a cooling rack to cool completely.
Pour the heavy cream into a chilled mixing bowl. Add the powdered sugar and vanilla extract. Using an electric mixer, whip the cream on medium-high speed until stiff peaks form, about 3 to 4 minutes.
Place one cake layer on your serving plate. Spread a generous layer of whipped cream over the top. Carefully place the second cake layer on top and frost the top and sides with the remaining whipped cream.
Use a grater or vegetable peeler to create chocolate shavings from a bar of dark chocolate. Sprinkle the shavings generously over the top of the cake. Chill the cake for at least an hour before slicing.