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). Grease a 9x13-inch baking dish.
Heat the butter in a large skillet over medium heat. Stir in the onion; cook and stir until the onion has softened and turned translucent, about 5 minutes. Reduce heat to medium-low, and continue cooking and stirring until the onion is golden brown, 10 to 15 minutes more. Meanwhile, combine eggs, salt, and pepper in a large bowl. Stir in the noodles and onion. Pour noodle mixture into the prepared baking dish and cover with aluminum foil.
Bake in the preheated oven until noodles are golden brown, 45 minutes to 1 hour.