Heat oil in deep 12-inch 5-quart saute pan over medium-high. Brown kielbasa 5 to 6 minutes, turning once; plate.
Reduce to medium; melt butter. Cook onion and cabbage with salt and pepper 10 to 12 minutes, stirring often, until softened with some browned edges.
Add broth; simmer. Stir in noodles; loosely cover and cook over medium-low 8 to 10 minutes, lifting and stirring every 2 minutes, until tender.
Add reserved water 2 tablespoons at a time only if drying before noodles finish. Return kielbasa; heat 2 minutes.
Remove from heat; add vinegar. Divide into 6 portions while noodles and cabbage remain loose and glossy.