Preheat oven to 350°F (175°C) and line a muffin pan with cupcake liners.
In a small bowl, whisk espresso powder into warm milk until fully dissolved.
In a separate bowl, whisk flour, baking powder, baking soda, and salt.
In a large bowl, beat butter, oil, and sugar together for 2–3 minutes until light and fluffy.
Add eggs one at a time, mixing well after each. Stir in vanilla extract.
Mix sour cream into the espresso milk.
Add dry ingredients and wet ingredients alternately to the batter, mixing just until combined.
Divide batter evenly, filling liners about ⅔ full.
Bake for 18–21 minutes, until tops spring back lightly and a toothpick shows a few moist crumbs.
Cool completely before frosting.