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Preheat oven to 350°F (175°C). Grease and flour three 9-inch cake pans. Line bottoms with parchment paper.
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Toast pecans and coconut for decoration. Set aside to cool.
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In a medium bowl, whisk together flour, baking soda, baking powder, and salt.
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In another bowl, beat egg whites with cream of tartar until stiff peaks form. Set aside.
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In a large bowl, cream butter and sugar until light and fluffy, about 5 minutes.
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Add egg yolks one at a time, beating well after each addition.
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Mix in vanilla and almond extracts.
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Alternate adding flour mixture and buttermilk to butter mixture, beginning and ending with flour (3 additions of flour, 2 of buttermilk).
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Fold in coconut and chopped pecans.
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Gently fold in beaten egg whites until just combined.
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Divide batter evenly between prepared pans.
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Bake for 25-30 minutes or until a toothpick comes out clean.
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Cool in pans for 10 minutes, then remove to wire racks to cool completely.