Let eggs stand at room temperature for 30 minutes. This helps them whip better and creates a lighter batter.

Preheat oven to 350°F. Line a standard 12-cup muffin pan with paper liners.

In a large mixing bowl, cream shortening, butter, and sugar together on medium speed for 3–5 minutes until light, pale, and fluffy. Scrape down the bowl often.

Add egg yolks one at a time, beating well after each addition (about 20 seconds per yolk). The mixture should look smooth and creamy.

Stir in vanilla extract and almond extract by hand or on low speed until just combined, about 30 seconds.

In a small bowl, whisk together flour, cornstarch, baking soda, and salt.

Add half of the dry ingredients to the creamed mixture on low speed, mixing for about 30 seconds until just combined.

Pour in half of the buttermilk and mix on low speed for about 30 seconds until the batter is smooth.

Add the remaining dry ingredients and mix on low speed for about 30 seconds.

Add the remaining buttermilk and mix on low speed for about 30 seconds, just until the batter is combined. Do not overmix. Checkpoint: You are ready to move on when the batter is smooth with no white streaks of flour visible.

In a separate small bowl, beat the egg whites on high speed for 2–3 minutes until stiff peaks form (when you lift the beaters, the peaks should stand straight up and not fall over).

Gently fold the egg whites into the batter in three additions using a rubber spatula. Turn the spatula upside down, cut down through the center, and fold the batter up and over. Rotate the bowl 90 degrees and repeat 15–20 times per addition. The batter should be light and fluffy with only small white streaks of egg white visible after the final fold. Checkpoint: You are ready to move on when the egg whites are mostly incorporated and the batter is light.

Fold in the flaked coconut and finely chopped pecans using the same gentle folding technique until evenly distributed, about 30 seconds.

Fill each paper-lined muffin cup three-fourths full (about 3 tablespoons of batter per cup). This leaves room for the cupcakes to rise.

Bake at 350°F on the middle rack for 20–25 minutes until a toothpick inserted in the center of a cupcake comes out clean (no wet batter clinging to it). The cupcakes should be lightly golden brown on top and spring back when lightly touched. Checkpoint: You are ready to move on when the toothpick comes out clean and the tops are set.

Let cupcakes cool in the muffin pan for 10 minutes (they will set enough to handle). Gently pop each cupcake out of the pan and place on a wire rack.

Allow cupcakes to cool completely at room temperature for 45–60 minutes before frosting. They should feel cool to the touch.

While cupcakes cool, make the frosting: In a medium bowl, beat softened cream cheese and butter together on medium speed for 2 minutes until smooth and creamy. Scrape down the bowl.

Add vanilla extract and almond extract, beating on low speed for 30 seconds.

Gradually add confectioners' sugar, 1/4 cup at a time, beating on low speed after each addition for about 30 seconds. After all sugar is added, increase speed to medium and beat for 1–2 minutes until the frosting is light, fluffy, and spreadable. It should hold soft peaks. Checkpoint: You are ready to move on when the frosting is smooth, fluffy, and holds its shape.

Spread or pipe about 2–3 tablespoons of frosting onto each cooled cupcake, mounding slightly in the center.

Top each frosted cupcake with a small handful of chopped pecans, pressing gently so they stick to the frosting.

Refrigerate frosted cupcakes for at least 1 hour before serving so the frosting sets and firms up.