Preheat the oven to 350°F and line four muffin cups with paper liners.
In a bowl, whisk together the flour, cocoa powder, sugar, and baking powder.
Add the egg, vegetable oil, milk, and vanilla extract to the dry ingredients. Stir until the batter is smooth and no streaks remain.
Divide the batter evenly among the four prepared muffin cups.
Bake for 18 to 20 minutes, or until a toothpick inserted in the center comes out clean. Let the cupcakes cool completely in the pan.
Spread a layer of chocolate frosting over each cooled cupcake.
Pipe small circles of white frosting on top of the chocolate layer. Drag a toothpick through the circles from the center outward to form the web pattern.