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Preheat the oven to 350 degrees. Line 18 muffin cups with cupcake liners and set pans aside.
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Sift the flour, baking powder, and salt together into a medium mixing bowl. Set aside.
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Beat the butter, sugar, and vanilla on medium speed in the bowl of a stand mixer fitted with the paddle attachment until mixture is light and smooth, 2 to 3 minutes.
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Place the white chocolate in a microwave-safe bowl and microwave on 50% power in 15-second intervals, stirring after each interval, until chocolate is melted and smooth. (This will take a couple of minutes but you need to melt the chocolate slowly so it doesn’t burn.) Add the white chocolate to the butter mixture and beat to combine. Scrape down the sides and bottom of the bowl with a rubber spatula.
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Turn mixer to low and add the flour mixture in three additions, alternating with the coconut milk, beginning and ending with the flour. (It will go flour, coconut milk, flour, coconut milk, flour.)
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Pour the batter into a large mixing bowl, then clean and dry the bowl of the stand mixer. (Be sure it’s very clean or your egg whites won’t whip properly.) Fit the mixer with the whisk attachment and beat on medium speed form soft peaks. Use a rubber spatula to gently fold the egg whites into the cake batter in three additions.
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Divide batter between the prepared muffin cups, filling each about 3/4 of the way full. Bake in the center of the oven for 18 to 22 minutes, until a cake tester inserted into the center of the cupcakes comes out clean. Let cool in pans for 10 minutes, then carefully transfer cupcakes to a wire rack to cool completely before frosting.