1/4 cup plus 2 tablespoons unsweetened cocoa powder (not Dutch process)
3/4 teaspoon baking soda
1/8 teaspoon salt
1 large egg
1/4 cup buttermilk
1 teaspoon pure vanilla extract
Preheat the oven to 350°. Line a 12-cup muffin tin with paper or foil liners.
In a medium saucepan, melt the butter with the vegetable oil and water over low heat.
In a large bowl, sift the flour with the sugar, cocoa powder, baking soda and salt. Add the melted butter mixture and beat with a handheld mixer at low speed until smooth. Add the egg and beat until incorporated, then add the buttermilk and vanilla and beat until smooth, scraping the bottom and side of the bowl. Pour the batter into the lined muffin tins, filling them about three-fourths full.
Bake the cupcakes in the center of the oven for about 25 minutes, until springy and a toothpick inserted in the center comes out clean. Let the cupcakes cool slightly, then transfer them to a rack to cool completely. Frost and top the cupcakes as desired. (See recipes for Chocolate Frosting, Marshmallow Frosting or White Buttercream Frosting.)
The unfrosted cupcakes can be wrapped in plastic and stored at room temperature for up to 2 days or frozen for up to 1 month.