Preheat oven to 350°F. Grease (with shortening) 3 (9-inch) round cake pans; line bottoms with parchment paper, and lightly grease paper with cooking spray. Dust pans with flour.

Stir together chopped chocolate and hot coffee in a medium microwavable bowl; microwave on HIGH until melted and smooth, 30 seconds to 1 minute, stirring mixture after 30 seconds. Set aside.

Whisk together flour, baking soda, and salt in a bowl. Beat butter and sugars with a heavy-duty stand mixer on medium speed until light and fluffy, about 3 minutes. Add yolks, 1 at a time, beating just until blended after each addition. Add melted chocolate mixture and vanilla; beat on low speed until blended. Add flour mixture alternately with buttermilk, beginning and ending with flour mixture. Beat on low speed just until blended after each addition.

Place egg whites in a separate clean bowl, and beat with an electric mixer on high speed until stiff peaks form, about 3 minutes; gently fold into batter. Divide batter among prepared pans.

Bake in preheated oven until a wooden pick inserted in center comes out clean, 24 to 28 minutes. Remove pans from oven; gently run a knife around outer edge of cake layers to loosen from sides of pans. Cool in pans on wire racks 15 minutes. Remove from pans to wire racks; discard parchment paper. Cool completely, 1 hour.

While the cake cools, prepare the Coconut-Pecan Frosting. Stir together evaporated milk, butter, granulated sugar, packed light brown sugar, and lightly beaten egg yolks in a heavy 3-quart saucepan. Cook over medium heat, stirring constantly, until butter melts and sugars dissolve, 3 to 4 minutes. Cook, stirring constantly, until mixture is bubbling and thick, 12 to 14 more minutes. Remove pan from heat; stir in sweetened flaked coconut, chopped toasted pecans, and vanilla extract. Transfer to a bowl. Let stand, stirring occasionally, until slightly warm and spreadable, about 40 minutes.

 Spread slightly warm Coconut-Pecan Frosting between layers and on top and sides of cake, if desired. Let stand until frosting is completely cool and set, about 15 minutes.