Preheat oven to 375°F. Lightly grease a 9x13-inch baking dish.
Spread ½ cup Thousand Island dressing on the bottom of the dish. Lay 3-4 lasagna noodles to cover (trim if needed). Top with half the sauerkraut, spread evenly.
Add a layer of corned beef (about half), overlapping slices for full coverage. Drizzle with ½ cup Thousand Island. Sprinkle ⅓ of the Swiss cheese over it.
Repeat: noodles, remaining sauerkraut, remaining corned beef, ½ cup Thousand Island, another ⅓ Swiss cheese.
Top with the last 3-4 noodles. Spread the remaining ½ cup Thousand Island evenly. Cover with the final ⅓ Swiss cheese.
In a small bowl, mix rye bread crumbs with melted butter; sprinkle over the cheese for a crispy top.
Cover tightly with foil and bake for 25 minutes. Remove foil and bake another 20-25 minutes until bubbly, golden, and the top is crisped.
Let rest 10-15 minutes before slicing. Sprinkle with chopped parsley. Slice into squares and serve hot.
