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Preheat the oven to 350 degrees. Line 16 to 18 muffin cups with paper liners and set pans aside.
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Whisk the flour, espresso powder, baking powder, and salt together in a medium bowl. Set aside.
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Place the butter in a large bowl and beat with an electric mixer until creamy. With mixer on medium speed, gradually beat in the sugar. Once the sugar is all added, scrape down the sides and bottom of the bowl and beat for a couple of minutes, until very light.
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Beat in the eggs and the vanilla.
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Turn mixer to low and beat in half of the dry ingredients until just combined, then beat in half of the sour cream and all of the milk.
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Beat in the remaining dry ingredients, again just until incorporated, then the remaining sour cream. The batter will be thick.
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Divide the batter between the prepared muffin cups, filling each about 2/3 full. Bake 18 to 24 minutes, until a cake tester inserted into the center of the cupcakes comes out clean.
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Cool the cupcakes in the pans for 5 minutes, then carefully transfer to a wire rack to cool completely before frosting.