Preheat your oven to 350°F and line a standard-sized cupcake pan with paper liners.

In a large bowl, whisk together the milk, vegetable oil, eggs, and vanilla.

Add the sugar and whisk to combine.

Next, add the flour, instant espresso powder, and baking powder. Mix just until no large lumps remain.

Divide the cake batter between the muffin tins, filling each one with about 1/4 cup of batter.

Bake for 15-17 minutes, or until a toothpick inserted into the center comes out clean.

Remove the cupcakes to a wire rack and cool completely before frosting.

Add the softened butter to the bowl of a stand mixer fitted with the paddle attachment. Beat on medium speed until the butter is smooth-- about 30 seconds.

With the mixer on low speed, slowly add the powdered sugar.

Once all of the powdered sugar has been incorporated, slowly add the espresso and vanilla extract.

Turn the mixer to medium-high speed and beat for 1-2 minutes, or until the frosting is light and fluffy.

Transfer the buttercream to a piping bag and frost the cooled cupcakes as desired.