In a large mixing bowl, combine vegetable oil, brown sugar, yogurt, vanilla extract, and white vinegar. Mix thoroughly until smooth. Gradually add the dry ingredients, including all-purpose flour, baking powder, baking soda, and cocoa powder. Pour in milk until a lumpy batter forms.

Preheat your oven to 400°F (220°C). Line a muffin tin with paper liners. Scoop the cupcake batter into the muffin cups, filling them about two-thirds full.

Bake for 5 minutes at 400°F, then reduce the temperature to 300°F (150°C) and bake for another 15-20 minutes until a toothpick inserted comes out clean.

Remove the muffin tin from the oven and allow it to cool for about 5 minutes. Transfer the cupcakes to a wire rack to cool completely.

In a chilled bowl, whip the heavy cream, granulated sugar, and vanilla extract until it reaches stiff peaks, about 3-5 minutes.

Frost each cupcake by piping a circular swirl and drawing lines from the center outward with a toothpick to create a spider web design.