Bring a large pot of lightly salted water to a boil. Cook the egg noodles in the boiling water until the pasta is tender yet firm to the bite, about 5 minutes. Drain.

While the noodles cook, melt the butter in a large skillet over low heat. Add the cabbage to the melted butter; season with salt and pepper. Cover and cook until the cabbage begins to brown, 5 to 7 minutes. Stir the drained noodles into the cabbage; cook and stir until the noodles begin to brown, about 5 minutes.