Fill a large pot with lightly salted water and bring to a rolling boil. Stir in egg noodles and return to a boil. Cook noodles uncovered, stirring occasionally, until tender but still slightly firm, about 5 minutes. Drain well.
Meanwhile, melt butter in a large skillet over medium-high heat and cook onion until soft and translucent, about 5 minutes. Add cabbage and cook until soft and almost brown, 15 to 20 minutes. Add cooked noodles and stir until it's hard to tell them apart from the cabbage, about 15 minutes more. Season with salt and pepper.