Preheat oven to 350° F and line a 12-cup muffin tin.
In a large bowl mix flour, sugar, cocoa powder, baking soda, orange zest, star anise, Sichuan peppercorns, and ginger together.
In a separate bowl, whisk together the vegetable oil, milk, vanilla, and vinegar. Add the wet ingredients to the dry ingredients and stir, just until combined.
Fill cupcake liners ¾ of the way, then bake for 15 to 20 minutes, until a toothpick inserted in the center comes out clean.
FOR THE FROSTING: Cream together butter until fluffy. Add sugar and cocoa powder about ½ cup at a time until blended. Mix in ginger, vanilla, and milk, adding more or less milk depending on desired consistency.
