Sprinkle cabbage with salt; let stand about 30 minutes. Squeeze dry; blot on paper towels.
Heat olive oil in 12-inch skillet; Add white onions; cook until they start to wilt. Stir in cabbage; saute, turning frequently, until tender, about 20 minutes. Season to taste with pepper. Transfer cabbage mixture and pan juices to large bowl; keep warm.
Cook noodles in boiling salted water until tender; drain. Quickly toss noodles with cabbage. Serve immediately.