Preheat the oven to 350°F (175°C) and grease a 9x13-inch baking pan.
Prepare the cake: In a large bowl, combine the German chocolate cake mix, eggs, water, and oil. Mix according to the package instructions until smooth.
Bake the cake: Pour the batter into the prepared pan and bake for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Cool the cake: Allow the cake to cool in the pan for about 10 minutes. Then, using the handle of a wooden spoon or a similar tool, gently poke holes all over the surface of the cake.
Add the filling: Pour the sweetened condensed milk evenly over the cake, allowing it to seep into the holes.
Prepare the frosting: In a saucepan, melt the butter over medium heat. Add the shredded coconut, chopped pecans, and vanilla extract. Stir to combine and remove from heat.
Top the cake: Spread the coconut-pecan frosting evenly over the cake.
Cool completely: Let the cake cool completely, allowing the flavors to meld together, before serving.