Preheat oven to 350°F (175°C).
In a large bowl, whisk together flour, baking powder, baking soda, salt, cocoa powder, and sugar.
Add the 13 tablespoons softened butter and mix until crumbly.
Add milk, water (or coffee), and vanilla to dry ingredients and mix until smooth.
Add eggs one at a time, beating well after each addition.
Scrape bowl and mix another 30 seconds. Batter will be thin.
Line muffin pans with cupcake liners.
Fill cupcake liners about ⅔ full (about ¼ cup batter per cupcake).
Bake for 18–22 minutes, or until a toothpick inserted in the center comes out clean.
Cool in the pan for 5 minutes, then transfer to a wire rack to cool completely before frosting.