Preheat and Prepare Pans: Preheat oven to 350°F (175°C). Grease and flour three 9-inch round cake pans. Line the bottoms with parchment paper.
Toast Nuts and Coconut: Toast 1½ cups of chopped pecans and 1½ cups shredded coconut for the cake. Toast 1 cup finely chopped pecans and 1 cup coconut for decoration. Let cool.
Whisk Dry Ingredients: Combine flour, baking soda, baking powder, and salt in a medium bowl. Set aside.
Beat Egg Whites: Beat egg whites with cream of tartar until stiff peaks form. Set aside.
Cream Butter and Sugar: Beat butter and sugar until light and fluffy (about 5 minutes).
Add Yolks and Extracts: Add egg yolks one at a time, then mix in vanilla and almond extracts.
Alternate Dry and Wet Ingredients: Add dry ingredients in 3 parts, alternating with buttermilk in 2 parts, beginning and ending with flour. Mix until just combined.
Fold in Nuts and Coconut: Gently fold in toasted pecans and shredded coconut.
Fold in Egg Whites: Carefully fold in beaten egg whites to maintain fluffiness.
Divide and Bake: Evenly pour batter into prepared pans. Bake 25–30 minutes, or until a toothpick comes out clean.
Cool Cakes: Cool in pans 10 minutes, then invert onto wire racks to cool completely.