Preheat the oven to 350°F and grease a 6-inch round cake pan.
In a mixing bowl, whisk together the flour, sugar, cocoa powder, baking soda, and salt.
Add the milk, vegetable oil, egg, and vanilla extract to the dry ingredients. Stir until the batter is smooth and no lumps remain.
Pour the batter into the prepared pan and bake for 25 to 28 minutes, until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 10 minutes, then turn it out onto a wire rack to cool completely.
Spread the chocolate buttercream frosting evenly over the top and sides of the cooled cake.
Spoon the vanilla frosting into a piping bag fitted with a small round tip. Pipe several concentric circles on top of the cake.
Drag a toothpick from the center outward through the circles at even intervals to create the spiderweb pattern.