Preheat the oven to 350°F (175°C). Grease and flour a 9×13-inch sheet pan.
In a large bowl, sift together the flour, sugar, baking soda, salt, and cocoa powder.
In a medium saucepan, combine the butter and water. Bring to a boil over medium heat, stirring occasionally.
Pour the hot butter and water mixture into the dry ingredients and stir until combined.
Add the buttermilk, eggs, and vanilla extract to the batter and beat until smooth.
Pour the batter into the prepared sheet pan and spread evenly.
Bake for 30 minutes or until a toothpick inserted in the center comes out clean.
While the cake bakes, prepare the frosting: In a medium saucepan, combine the sweetened condensed milk, butter, and egg yolks.
Cook over medium heat, stirring constantly, until the mixture thickens and turns golden, about 10 minutes.
Remove from heat and stir in the vanilla extract, shredded coconut, and chopped pecans. Let cool slightly.
When the cake is done, remove it from the oven and allow it to cool for 10 minutes.
Spread the coconut-pecan frosting evenly over the warm cake.
Allow the cake to cool completely before slicing and serving.