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Make Cake Rounds:
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Preheat oven to 350u00b0F with racks in upper and lower third. Line two baking sheets with parchment paper.
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Whisk together flour, cocoa powder, baking soda, and salt in a bowl.
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Beat butter, oil, and sugar with an electric mixer until combined well, about 2 minutes. Beat in egg, vanilla, and vinegar.
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Reduce speed to low and alternately mix in flour and buttermilk in batches, beginning and ending with the flour until combined.
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Add the red food coloring and mix on low speed until thoroughly combined.
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Spoon 2 tablespoon mounds of batter 2-inches apart on lined baking sheets.
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Bake, switching positions of baking sheets halfway through baking, until rounds are puffed and set, 8 to 10 minutes.
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Slide parchment with rounds onto wire racks to cool completely.
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Make Filling:
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Beat together cream cheese, butter, lemon juice, vanilla, salt, and sugar until creamy, 1 to 2 minutes. Spread about 2 tablespoons of filling on flat-side of half the rounds; top with remaining rounds, flat side down, to form whoopie pies.
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To get perfectly round whoopie pies, use a 2 tablespoon ice cream scoop with the cake batter.
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Store whoopie pies, chilled, in an airtight container, the layers separated between sheets of parchment paper, for up to 3 days. Bring to room temperature