Preheat the oven to 350°F (175°C). Grease and flour a 9x13-inch baking pan or spray with baking spray that contains flour.
In a large bowl, beat 1 cup softened butter and 2 cups sugar with an electric mixer until light and fluffy, about 3–4 minutes.
Add the 4 large eggs one at a time, beating briefly after each addition and scraping down the bowl as needed.
Beat in 1 teaspoon vanilla extract until combined.
Sift together 2 cups cake flour, 1/4 cup unsweetened cocoa powder, 1/2 teaspoon baking soda, and 1/2 teaspoon salt.
Add the dry ingredients to the butter mixture in three additions, alternating with 1 1/4 cups buttermilk, beginning and ending with the dry ingredients; mix just until combined.
Stir in the 1-ounce bottle of liquid red food coloring until the batter is uniformly colored. Pour batter into the prepared pan.
Bake for 35–40 minutes, or until a wooden pick inserted in the center comes out clean. Allow the cake to cool in the pan before frosting.
For the frosting, combine 1 1/2 cups heavy whipping cream, 1 1/2 cups sugar, 5 egg yolks, and 6 tablespoons butter in a medium saucepan.
Cook over medium heat, stirring frequently, until the mixture thickens enough to coat the back of a spoon.
Remove from heat and stir in 2 cups sweetened angel hair coconut and 1 1/2 cups chopped toasted pecans; let the frosting cool 15–20 minutes so it thickens slightly.
Pour or spread the cooled frosting evenly over the cooled cake, allowing it to set before slicing and serving.