FOR THE FROSTING: Whisk yolks in medium saucepan; gradually whisk in evaporated milk. Add sugars, butter, and salt and cook over medium-high heat, whisking constantly, until mixture is boiling, frothy, and slightly thickened, about 6 minutes. Transfer mixture to bowl, whisk in vanilla, then stir in coconut. Cool until just warm, cover with plastic wrap, and refrigerate until cool or cold, at least 2 hours or up to 3 days. (Pecans are stirred in just before cake assembly.)
FOR THE CAKE: Adjust oven rack to lower-middle position; heat oven to 350 degrees. Combine chocolate and cocoa in small bowl; pour boiling water over and let stand to melt chocolate, about 2 minutes. Whisk until smooth; set aside until cooled to room temperature.
Meanwhile, spray 13 by 9-inch baking pan with nonstick cooking spray. Line bottom of pan with parchment or waxed paper and spray. Dust pan with flour, and knock out excess. Sift flour and baking soda into medium bowl or onto sheet of parchment or waxed paper.
In bowl of standing mixer, beat butter, sugars, and salt at medium-low speed until sugar is moistened, about 30 seconds. Increase speed to medium-high and beat until mixture is light and fluffy, about 4 minutes, scraping down bowl with rubber spatula halfway through. With mixer running at medium speed, add eggs one at a time, beating well after each addition and scraping down bowl halfway through. Beat in vanilla; increase speed to medium-high and beat until light and fluffy, about 45 seconds. With mixer running at low speed, add chocolate, then increase speed to medium and beat until combined, about 30 seconds, scraping down bowl once (batter may appear broken). With mixer running at low speed, add dry ingredients in 3 additions, alternating with sour cream (in 2 additions), beginning and ending with dry ingredients, and beating in each addition until barely combined. After final flour addition, beat on low until just combined, then stir batter by hand with rubber spatula, scraping bottom and sides of bowl to ensure that batter is homogenous (batter will be thick). Pour into prepared pan and level with rubber spatula.
Bake cake until toothpick inserted into center of cake comes out clean, 30 to 35 minutes. Cool in pan 10 minutes, then invert cake onto greased wire rack; peel off and discard paper. Cool cake to room temperature before frosting, about 2 hours. (Cooled cake can be wrapped in plastic wrap and stored at room temperature for up to 1 day.).
To Frost the Cake: Stir toasted pecans into chilled frosting. Invert cake onto serving platter. Using spoon, place dollops of frosting evenly spaced over cake. Using icing spatula, spread frosting evenly over surface of cake. Cut into squares and serve. (Cover leftovers and refrigerate for up to 3 days. If refrigerated longer than 2 hours, let cake stand at room temperature 15 to 20 minutes before serving.).