Fill a large saucepan with lightly salted water then bring to a rolling boil over high heat. Once the water is boiling, stir in the egg noodles then 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 180 degrees C.
Heat 1 tablespoon of the vegetable oil in a frypan 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 then continue cooking and stirring until the onion is golden brown, 10 to 15 minutes more. Combine the noodles, onion, eggs, remaining vegetable oil, salt and pepper in a large bowl. Pour mixture into an square baking dish.
Bake in the preheated oven until firm, about 35 minutes.
During Passover, use kosher for Passover egg noodles.