Fill a large pot with lightly salted water and bring to a rolling boil over high heat. Once the water is boiling, stir in the egg noodles, and return to a boil. Cook the pasta uncovered, stirring occasionally, until the pasta has cooked through, but is still firm to the bite, about 5 minutes. Drain well in a colander set in the sink.
Preheat an oven to 350 degrees F (175 degrees C). Butter a 9x13-inch baking dish.
Beat the eggs, milk, sugar, and vanilla extract together in a bowl. Stir in the noodles. Pour the noodle mixture in the prepared baking pan. Pour the melted butter over the noodles, then top with the coconut.
Bake in the preheated oven until the noodles are set and the coconut is golden brown, about 1 hour.
