Preheat the oven to 350°F (175°C). Grease three 8- or 9-inch round cake pans, line the bottoms with parchment rounds, then grease and lightly flour the parchment and sides.

Spread the chopped pecans for the cake (1 cup / 110 g) on a baking sheet and toast for 6–8 minutes, stirring once, until fragrant and slightly darker. Let cool completely.

Separate the 5 eggs, placing whites in a clean mixing bowl and yolks in a small bowl. Using a hand mixer or stand mixer with the whisk attachment, beat the egg whites on medium-high speed until stiff peaks form. Set aside.

In a large mixing bowl, beat the softened butter, shortening, and granulated sugar together on medium-high speed for 3–4 minutes, until very light and fluffy, scraping down the bowl as needed.

Beat in the egg yolks one at a time, mixing well after each addition. Add the vanilla extract and beat until the mixture looks thick, pale, and creamy.

In a separate bowl, whisk together the flour, baking soda, and salt until well combined.

On low speed, add the dry mixture to the creamed mixture in 3 additions, alternating with the buttermilk in 2 additions (dry–buttermilk–dry–buttermilk–dry). Mix just until combined after each addition to avoid over-mixing.

Using a spatula, gently fold the shredded coconut and 1 cup cooled toasted chopped pecans into the batter. The batter will be thick and rich.

Gently fold the whipped egg whites into the batter in 2–3 additions, using light, sweeping motions from the bottom of the bowl upward, until just incorporated.

Divide the batter evenly among the three prepared pans. Bake for 22–28 minutes, or until the tops are lightly golden and a toothpick inserted in the center comes out with just a few moist crumbs.

Let the cakes cool in the pans for 10–15 minutes. Run a knife around the edges, turn them out onto wire racks, peel off the parchment, and let cool completely before frosting.

In a large bowl, beat the softened cream cheese and butter together on medium-high speed until completely smooth and creamy, 2–3 minutes. On low speed, gradually add the powdered sugar 1–2 cups at a time, then increase to medium and beat until smooth. Beat in the vanilla and salt. If the frosting is too soft, chill for 20–30 minutes.

Place one cooled cake layer on a serving plate. Spread a generous layer of cream cheese frosting over the top. Add the second layer and more frosting, then the third layer. Frost the top and sides with a thin crumb coat, chill for about 20 minutes, then add a final thick layer of frosting.

Fold some of the toasted chopped pecans (from the frosting amount) into the remaining frosting if desired. Press extra shredded coconut and chopped pecans onto the sides of the cake or sprinkle over the top. Optionally, arrange pecan halves around the edge for decoration. Chill the finished cake for at least 30–60 minutes before slicing for the neatest layers.