Preheat the oven to 350°F and line a cupcake tin with four paper liners.
In a mixing bowl, whisk together the flour, cocoa powder, sugar, and baking powder.
Add the egg, ¼ cup milk, vegetable oil, and ½ teaspoon vanilla extract. Stir until the batter is smooth.
Divide the batter evenly among the four liners. Bake for 18-20 minutes until a toothpick comes out clean. Let the cupcakes cool completely.
In a clean mixing bowl, beat the softened butter with the powdered sugar, remaining ½ teaspoon vanilla extract, and 2 tablespoons milk until creamy.
Frost each cooled cupcake with a base layer of white frosting.
Mix a small amount of black food coloring into the remaining frosting. Pipe thin circles on top of each cupcake, then drag a toothpick from the center outward to form the web pattern.