In large skillet, heat oil over medium-high heat. Add onions; sauté until softened (about 3-5 minutes). Add sauerkraut to skillet; salt and pepper to taste.
Sauté until browned (about 10-12 minutes). Stir in cheese, dressing and Worcestershire; cook until cheese is melted.
Meanwhile, prepare hot dogs as desired; place hot dogs in buns and top with Reuben sauce.
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