Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 13x9-inch baking pan.

Beat cake mix, water, eggs, oil, and 1/3 cup sweetened condensed milk in a large bowl with an electric mixer on low speed until moistened. Beat on high speed for 2 minutes. Pour batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center of cake comes out clean, 40 to 45 minutes.

Meanwhile, combine remaining sweetened condensed milk, butter, and egg yolk in a medium saucepan over medium heat; cook and stir until thickened, about 6 minutes. Add pecans, coconut, and vanilla; mix well. Allow frosting to cool slightly.

Spread frosting over warm cake. Store leftovers covered in the refrigerator.