Preheat an oven to 350 degrees F (175 degrees C). Lightly grease one baking sheet and one 9×13-inch baking dish.
Bake the butter squash on the prepared baking sheet, cut side down, in the preheated oven until tender, about 50 minutes.
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.
Heat the olive oil in a 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 very tender and dark brown, 15 to 20 minutes more.
Beat eggs and egg whites lightly in a large bowl. Stir in the noodles and onion. Scoop the flesh from the butternut squash into the noodle mixture. Season with rosemary, sage, salt, and pepper. Gently mix to combine. Pour mixture into the prepared 9×12-inch baking pan. Sprinkle with chopped pecans.
Bake in the preheated oven until golden brown, about 30 minutes. Serve warm or at room temperature.