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1
Preheat the oven to 350F. Line muffin tins with paper liners and set aside.
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2
Sift the cake flour into a large bowl (or into the bowl of a stand mixer, if you have one). Add sugar, baking powder, and salt. Stir gently to combine. With the mixer on low, add butter cubes a few at a time and beat until you have a sandy, coarse texture.
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3
In another bowl, whisk together egg whites, coconut milk, shredded coconut, and vanilla (and lime juice, if using). Add half of the mixture to the dry ingredients and beat on medium-high speed until well combined, about a minute. Add the remaining wet mixture and then beat until the batter is light and fluffy, about 30 seconds.
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4
Scoop batter evenly into the liners so they're about 2/3 full (I use a quarter cup measuring cup and that's usually about right). Bake for 18 minutes, or until they spring under your fingertips when pressed lightly. Allow to cool in the pans slightly before transferring baked cupcakes to a rack to cool completely.
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5
To make the frosting, add egg whites and sugar into a large bowl (or the bowl of a stand mixer if you have one) and whisk to combine. Set the bowl over a pan of gently simmering water and heat, whisking constantly, until the mixture is hot to the touch and the sugar has dissolved -- about 6 to 8 minutes. If you rub a little bit between your fingers, it shouldn't feel grainy to the touch.
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6
Transfer the bowl to a stand mixer (with a whisk attachment) if you have one, or else set on a towel on your counter, and start whipping. Beat on medium-high speed until the mixture is a fluffy meringue and the bowl is cool to the touch (6 to 8 minutes if using a stand mixer, 10 to 15 if using a hand mixer).
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7
With the mixer on low, start adding butter cubes one at a time until they've all been added to the meringue. Increase the speed back to medium-high and continue beating until butter is fully incorporated, smooth, and fluffy (don't worry if it looks curdled - more beating will bring it together!).
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8
Slowly add the coconut milk, vanilla and salt to the meringue and beat on medium-high speed until the coconut milk is incorporated and the mixture is once again fluffy and smooth. It'll take some time to reconstitute itself, so be patient!
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9
To frost, transfer frosting to a piping bag with a decorative tip (or a ziplock with the corner cut out; or smear some on with a knife) and pipe onto each cupcake. You can store these at room temp for up to 3 days in an air-tight container.
