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Preheat the oven to 350 degrees. Line 16 muffin cups with cupcake liners and set pans aside.
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Whisk the flour, baking powder, baking soda, and salt together in a medium mixing bowl.
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Place the butter in a large mixing bowl and beat with an electric mixer set to medium speed until very creamy. Add the sugar and vanilla and beat until well combined. Scrape down the sides and bottom of the bowl, then add the eggs 1 at a time, beating well after each addition. Add the flour mixture in 3 additions, alternating with the sour cream, beginning and ending with the flour. (It will go flour, sour cream, flour, sour cream, flour.) Fold in the lemon zest; batter will be very thick.
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Fill the prepared muffin cups with about 1/4 cup of batter and bake 20 to 25 minutes, until a toothpick inserted into the center of the cupcakes comes out clean. Cool completely on wire racks before filling and frosting.