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Make the cake: Place the 2 sticks unsalted butter for the cake in the bowl of a stand mixer or a large bowl if using a hand mixer. Place 4 large eggs and 1 cup buttermilk for the cake and the 2 sticks unsalted butter for the frosting on the counter to let them sit out at room temperature.
Coarsely chop 4 ounces semisweet chocolate if needed. Place the chocolate or chocolate chips in a small saucepan. Add 1/2 cup water and heat over low heat, stirring constantly, until fully melted, 2 to 3 minutes. Remove from the heat and let cool to room temperature, 10 to 15 minutes. Meanwhile, preheat the oven.
Arrange a rack in the middle of the oven and heat the oven to 350°F. Coat 2 (9-inch) round cake pans with cooking spray and line the bottoms with parchment paper.
Add 2 cups granulated sugar to the bowl of butter and beat with the paddle attachment or hand mixer on medium-high speed until light and fluffy, 2 to 3 minutes. Beat in the 4 eggs one at a time, waiting until each one is fully incorporated before beating in the next. Slowly beat in 2 teaspoons vanilla extract and the melted chocolate, and continue beating until the mixture is smooth, 2 to 3 minutes.
Turn the mixer off. Add 2 1/4 cups all-purpose flour, 1 1/4 teaspoons kosher salt, and 1 teaspoon baking soda. Mix on low speed until incorporated, 1 to 2 minutes. With the mixer still running, gradually add the buttermilk and continue mixing until the batter is completely smooth, scraping down the sides halfway through mixing, 2 to 3 minutes total.
Evenly divide the batter between the prepared baking pans (about 14 ounces per pan) and smooth the tops. Bake until the cakes are lightly browned and a toothpick inserted into the center comes out with only a few moist crumbs attached, 35 to 40 minutes. Place the pans on a wire rack and let the cakes cool completely in the pans. Meanwhile, make the filling.
Make the filling: Place 1 cup packed light brown sugar, 1 stick unsalted butter, 3 large egg yolks, 1 cup evaporated milk, 1 teaspoon vanilla extract, and 1/4 teaspoon kosher salt in a medium saucepan. Bring mixture to a boil over medium heat and cook until sugar is completely dissolved and mixture is thick enough to coat the back of a spoon, 3 to 4 minutes.
Remove the pan from the heat. Stir in 2 cups chopped, toasted pecans and 1 packed cup shredded, unsweetened coconut. Set aside to cool to room temperature while you make the frosting.
Make the frosting: Place the 2 sticks room temperature unsalted butter in the clean bowl of a stand mixer fitted with a whisk attachment. (Alternatively, use an electric hand mixer and large bowl.) Add 1/2 cup unsweetened cocoa powder, 1/4 cup heavy cream, 1 teaspoon vanilla extract, and 1/4 teaspoon kosher salt. Beat on low speed until smooth, 3 to 4 minutes.
Turn the mixer off. Add 3 1/2 cups powdered sugar and mix on low speed until combined, 1 to 2 minutes. Increase the speed to high and beat until the frosting is light, fluffy, and doubled in volume, scraping down the sides of the bowl down halfway through, 3 to 4 minutes total. Transfer 1 cup of the frosting to a small zip-top bag and set aside.
Assemble the cake: Remove the cakes from the pans and discard the parchment. Using a serrated knife, trim the rounded tops off of each cake. Place one cake layer, cut-side down, onto a serving platter or cake stand. Dollop 1 cup of the frosting onto the cake and smooth into a thin, even layer with an offset spatula, going all the way to the edges. Top with half of the coconut filling and gently spread all the way to the edges.
Top with the remaining cake layer, cut-side down. Frost the top and sides of the cake with the remaining frosting. Snip off one bottom corner of the bag of frosting. Pipe small, decorative mounds of the frosting around the top of the cake. Dollop the remaining coconut filling onto the top of the cake and gently smooth into a thin, even layer all the way to the mounds of frosting.