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Preheat oven to 350ºF. Lightly grease and flour 3 8-inch round cake pans lined with parchment paper (you can also use 2 9-inch but will want to bake longer).
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In a large bowl, sift together the cake flour, baking powder, baking soda, and salt. Set aside.
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With your mixer (I use the paddle attachment), cream together the butter and sugar on medium-high speed until very light and fluffy (3-5 minutes).
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Add the two eggs, one at a time, beating well after each addition.
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Add the vanilla extract and beat well to combine.
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Starting and ending with flour, with your mixer on LOW speed, alternately add flour mixture and buttermilk until just combined.
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In a large clean bowl, (I transfer the batter to a bowl and clean my mixing bowl thoroughly to use here with my wire attachment) beat the egg whites until stiff peaks form.
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Gently fold 1/3 of the whites into batter, followed by another 1/3 of the egg whites, and then the remaining whites.
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Gently fold the sprinkles into the batter.
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Divide evenly into prepared pans.
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Bake at 350ºF for 18 to 20 minutes, or until the cake slightly pulls away from the sides or until a toothpick inserted into the center of the cake comes out clean.
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Let cool in pans 10 minutes and then remove to a wire rack to cool completely.
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Once cake layers are cooled, clean an 8-inch cake pan and line with saran wrap or foil. Place a layer of cake in prepared pan, then gently spread 2 8-ounce containers of cookie dough on top to cover completely. Gently pull out layer using saran wrap/foil and place on cake platter or stand. Repeat with a second layer and place on top of the first, then add third cake layer to the top.