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Place a rack in the middle of the oven and preheat the oven to 350°F. Line a 12-cup muffin pan or 24-cup mini-muffin pan with paper liners and lightly grease the papers.
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Whisk together the flour, baking powder, and salt. Set aside.
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In a stand mixer fitted with a paddle attachment (or using an electric beater), mix the butter and baking sugar alternative on medium speed for 1 1/2 to 2 minutes; the mixture will be crumbly.
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Scrape the bottom and sides of the bowl and add the egg, beating on high speed for 1 minute.
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Add the dry ingredients in two additions alternately with the milk, mixing on medium speed for 30 seconds and scraping the bowl between each addition. Don’t worry if the batter still looks a bit lumpy.
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Add the vanilla and mix on medium speed for 1 minute, until the batter is smooth.
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Scoop 1/4 cup of batter into each of the standard muffin cups or 2 teaspoons batter into each of the mini-muffin cups; a muffin scoop or teaspoon cookie scoop are handy tools here. (If you're baking mini cupcakes, you'll need to bake the batter in two batches.)
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Bake the cupcakes or mini cupcakes until a toothpick inserted into the center of one comes out clean, 16 to 18 minutes for the standard cupcakes or 10 to 11 minutes for the mini cupcakes.
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Remove the cupcakes from the oven and cool them in the pan for 15 minutes before transferring them to a rack to cool completely. Note: If you're baking mini cupcakes, let the pan cool before scooping and baking the remainder of the batter.
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Store cupcakes, well wrapped, at room temperature for 2 to 3 days. Freeze for longer storage.