1 Preheat oven and prep muffin tin: Preheat oven to 350°F with a rack in the middle position. Prepare a muffin tin with cupcake liners.
2 Whisk dry ingredients: In a large bowl, vigorously whisk together the flour, cocoa powder, sugar, baking soda, and salt until there are no visible clumps (cocoa tends to clump up).
3 Mix wet ingredients: In a separate bowl, mix together the coffee (or water plus coffee granules), vinegar, vanilla extract, and olive oil.
4 Pour the wet ingredients into the dry ingredients and stir only until they just come together. Do not over-beat! The mixture should be thin and rather lumpy.
5 Ladle the batter into the cupcake liners, filling them about two-thirds of the way full.
6 Bake: Place in oven and bake at 350°F for 18 to 20 minutes, until a bamboo skewer inserted in the center comes out clean.
7 Remove from oven and let cool in the pan for 5 minutes, then remove from pan and let cool on a rack. Once cool, you can eat plain, sprinkle with powdered sugar, or drizzle or coat with frosting.
While the cupcakes are cooking, make the frosting. Melt butter in a small saucepan and remove from heat. Stir in the cocoa until smooth. Sprinkle in about a third of the powdered sugar, stir, then sprinkle in about a half of the milk. Keep alternating with the powdered sugar and either milk or vanilla, stirring after each addition, until the frosting is the consistency you want, and smooth. If it’s too runny, add more powdered sugar. If too stiff, add a little more milk or vanilla extract.
To pipe in a decorative pattern, scoop the frosting into the corner of a ziplock freezer bag. Use scissors to cut away 1/4-inch or so from the tip of the corner. Then just squeeze the frosting out of the bag onto the cupcakes in any design you like.