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Preheat oven to 325°F. Lightly grease and flour a 12-cup bundt cake pan.
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Whisk together flour, cocoa powder, baking soda, and salt in a medium bowl.
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Beat egg whites in a large bowl at high speed with an electric mixer until stiff peaks form.
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In a separate large bowl, beat butter and shortening until creamy. Gradually add sugar and beat well to combine.
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Add egg yolks, one at a time, beating well after each addition.
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Add flour mixture in three additions, alternatively with buttermilk in two additions, mixing on low speed until just combined. Do not over-mix.
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Stir in vanilla, coconut, and pecans. Fold in egg whites.
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Pour batter into prepared pan. Bake for 55 to 60 minutes or until a toothpick or cake tester inserted in the center comes out clean.
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Cool cake in pan for 12 minutes. Remove cake from pan and cool completely on a wire rack.