Preheat the oven to 350°F (175°C). Grease and flour the 9x13 inch baking pan.
In a large mixing bowl, combine the flour, sugar, cocoa powder, baking powder, baking soda, and salt. Mix well.
Add the eggs, milk, oil, and vanilla extract to the dry ingredients. Beat on medium speed for about 2 minutes until well combined.
Carefully stir in the boiling water. The batter will be thin.
Pour the batter into the prepared baking pan and bake for 30 minutes or until a toothpick inserted in the center comes out clean.
Once the cake is done, let it cool for about 15 minutes in the pan. Using a poking utensil, poke holes all over the cake, about 1 inch apart.
Pour the sweetened condensed milk mixture over the warm cake, ensuring it seeps into the holes. Allow the cake to cool completely.
For the frosting, combine sugar, butter, evaporated milk, egg yolks, and vanilla extract in a saucepan over medium heat. Whisk continuously until the mixture thickens (about 10-12 minutes).
Remove from heat and stir in the coconut and pecans. Let the frosting cool for a few minutes before spreading over the cooled cake.
Refrigerate the cake for at least an hour before serving to allow the flavors to meld.