Bring a large pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally until cooked through but firm to the bite, about 5 minutes. Drain.

Melt butter in a skillet over low heat; cook and stir onion until onion is softened and butter is golden brown, 5 to 10 minutes. Add cabbage and toss to coat. Place a lid on the skillet; cook cabbage mixture, stirring occasionally, until cabbage is tender, about 30 minutes. Season with salt and pepper. Remove lid and continue to cook until cabbage begins to brown, 5 to 10 more minutes.

Mix noodles and cabbage together in a serving bowl; season with salt and pepper.