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Preheat oven to 350°F. Coat a 13x9x2-inch baking pan with cooking spray; set aside. In a large bowl, whisk together eggs, milk, salt and pepper until combined. Pour into the prepared baking pan. Bake about 10 minutes or until egg mixture is set. Remove from oven and cool slightly. Cut into eight rectangles.
To assemble sandwiches, spread cut sides of muffins with salad dressing. Place egg rectangles on the bottom halves of muffins, folding to fit. Top with sauerkraut; add corned beef and cheese. Replace top halves of muffins. Wrap each sandwich in heavy foil and chill overnight.
When ready to serve, prepare grill (with a cover). For a charcoal grill, arrange medium-hot coals around edge of grill. Test for medium heat above center of grill. Place foil-wrapped sandwiches on grill rack over center of grill. Cover and heat for 15 to 20 minutes or until heated through, turning once halfway through grilling. (For a gas grill, preheat grill. Reduce heat to medium. Adjust for indirect cooking and heat as above.)