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Preheat oven to 350 F. Line a muffin pan with cupcake liners.
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In a bowl, whisk together the flour, baking powder, and salt. Set aside.
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In a large bowl, beat sugar and butter together on medium speed until light and fluffy.
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Reduce to low speed and add the egg and egg white to the butter mixture one at a time. Beat well after each, and add in vanilla.
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Add the flour mixture to the butter mixture in three additions, alternating with the champagne in two additions. Beat until just combined, being careful not to over beat.
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Divide the batter evenly into the prepared muffin pan, filling each about ¾ of the way full.
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Bake for 18-20 minutes or until a toothpick inserted in the center comes out clean.
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While the cupcakes bake, start the champagne reduction for the frosting. In a small saucepan, bring the 1-cup of champagne to a boil over medium-high heat. Once it’s reached a boil, reduce the heat to medium and allow to simmer until reduced to about ¼ cup (8-10 minutes). Once reduced, reserve 2-3 tablespoons for the frosting and use the rest to brush the tops of the warm cupcakes.
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Let cupcakes cool completely on a wire rack.