01 - Whisk together eggs, heavy cream, salt, and pepper in a medium bowl until fully combined and slightly frothy.
02 - Heat a nonstick skillet over medium heat. Add a small amount of butter and pour in just enough egg mixture to coat the bottom, swirling to create a thin, even layer. Cook for 1-2 minutes until set, then carefully flip and cook an additional 10-20 seconds. Remove to a plate and repeat with remaining batter to make approximately 4 wraps.
03 - Lay each cooked egg wrap flat on a clean surface. Spread 1 tablespoon of dressing across the center of each wrap, leaving a small border around the edges.
04 - Layer chopped corned beef evenly over the dressing, followed by a spoonful of drained sauerkraut and a generous sprinkle of shredded Swiss cheese.
05 - Fold in the sides of each wrap and roll tightly from bottom to top, enclosing the filling completely. For a melty finish, return the roll ups to the warm skillet for 1-2 minutes to heat through and melt the cheese.
06 - Slice each roll up in half diagonally, sprinkle with fresh parsley if desired, and serve immediately with additional dressing on the side for dipping.