Heat the oven to 350°F. Spray the bottoms and sides of three 8-inch or 9-inch round cake pans with the cooking spray. Cut three 8-inch or two 9-inch rounds of waxed paper or cooking parchment paper. Line bottoms of pans with the paper.
Coarsely chop the chocolate. In a 1-quart saucepan, heat the chocolate and water over low heat, stirring frequently, until chocolate is completely melted; remove from heat and cool.
Meanwhile, in a medium bowl, stir the flour, baking soda and salt until mixed; set aside. In another medium bowl, beat 2 cups sugar and 1 cup butter with an electric mixer on medium speed until light and fluffy; set aside.
Place an egg separator over a small bowl. Crack 1 egg over the separator to separate the yolk from the white. Separate 3 more eggs. Place yolks in a small bowl. (Save the whites for another recipe.)
On medium speed, beat 1 egg yolk at a time into the sugar mixture until mixed. On low speed, beat in the melted chocolate and 1 teaspoon vanilla. On low speed, beat in 1/2 of the flour mixture just until smooth, then beat in 1/2 of the buttermilk just until smooth. Repeat beating in flour mixture alternately with the buttermilk just until smooth.
Wash and dry mixer beaters. In a small bowl, beat the eggs whites on high speed until beaten eggs whites form stiff peaks when beaters are lifted. Add egg whites to the batter; to fold in, use a rubber spatula to cut down vertically through the batter, then slide the spatula across the bottom of the bowl and up the side, turning batter over. Rotate the bowl 1/4 turn, and repeat this down-across-up motion. Continue folding until batter and egg whites are blended.
Pour batter into pans; use a rubber spatula to scrape batter from bowl, spread batter evenly in pans and smooth top of batter. (If batter is not divided evenly, spoon batter from one pan to another.) Refrigerate batter in third pan if not all pans will fit in oven at one time; bake third pan separately.
Bake 8-inch pans 35 to 40 minutes, 9-inch pans 30 to 35 minutes, or until a toothpick inserted in the center comes out clean.
Cool cakes in pans 10 minutes. To remove cake from pan, invert onto cooling rack, then invert right side up on second cooling rack. Cool completely, about 1 hour.
Separate the 3 eggs; save the egg whites for another recipe. In a 2-quart saucepan, stir the egg yolks, 1 cup sugar, 1/2 cup butter, the evaporated milk and 1 teaspoon vanilla until well mixed. Cook over medium heat about 12 minutes, stirring frequently, until thick and bubbly. Stir in the coconut and pecans. Cool about 30 minutes, beating occasionally with a spoon, until mixture is spreadable.
Place 1 cake layer, rounded side down, on a cake plate; using a metal spatula, spread 1/3 of the filling over the layer. Add second layer, rounded side down; spread with 1/3 of the filling. Add third layer, rounded side up; spread with remaining filling, leaving side of cake unfrosted. Store cake covered in the refrigerator.