Core a head of cabbage and blanch whole leaves in boiling water for 2–3 minutes until soft. Drain and pat dry.
Heat olive oil in a pan over medium heat. Add onions and garlic and sauté until translucent, about 3–4 minutes. Let cool slightly.
In a large bowl, mix ground beef or shredded corned beef, sauerkraut, Swiss cheese, sautéed onions and garlic, caraway seeds, salt, and pepper until well combined.
Lay out one cabbage leaf, place ⅓–½ cup of filling in the center, fold in the sides, and roll up snugly. Repeat with remaining leaves and filling.
Spread a thin layer of the sauce (mixed Russian dressing and ketchup) on the bottom of a baking dish. Arrange rolls seam side down.
Top the rolls with the remaining sauce, spreading evenly.
Cover with foil and bake at 350°F (175°C) for 25 minutes.
Remove foil, sprinkle with extra cheese if desired, and bake uncovered for 10 more minutes until bubbly and golden.
Let rest for 5 minutes before serving. Garnish with fresh parsley or dill and serve with extra Russian dressing on the side.