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Preheat the oven to 350 degrees. Line 17 to 18 muffin cups with paper liners and set pan aside.
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Stir together the flour, cocoa powder, baking soda, and salt in a small bowl. Set aside.
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Combine the sugar, oil, egg, vanilla, and vinegar in a large bowl. Beat with an electric mixer set to medium until very smooth, about 2 minutes. Stop to scrape down the sides and bottom of the bowl as necessary.
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With mixer on low, gradually add the dry ingredients and beat until just incorporated. Scrape down the sides and bottom of the bowl.
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Again with mixer on low, beat in the buttermilk, then the food coloring. Stir a few times with a rubber spatula to make sure all the ingredients are mixed in.
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Pour a scant 2 tablespoons of red velvet batter into each muffin cup. Top with 1 heaping tablespoon of the cream cheese mixture, then another 2 tablespoons red velvet.
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Bake for 20 to 25 minutes, until cupcakes spring back when lightly pressed with your fingertip.
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Cool cupcakes in muffin tins for 15 minutes, then remove to a wire rack to cool completely before frosting them.