Preheat the oven to 350°F. Lightly coat a 9-by-13-inch baking dish or rimmed sheet pan with nonstick cooking spray.
Coat a large nonstick skillet with cooking spray and heat it over medium-low heat.
Whisk together the eggs, egg whites and black pepper. Pour the mixture into the skillet and cook, stirring gently, until the eggs are softly set. Remove the skillet from the heat.
Keep the rolls connected and use a serrated knife to slice the entire package horizontally. Place the bottom half of the rolls in the prepared baking dish.
Spread the scrambled eggs evenly over the rolls. Sprinkle the turkey sausage crumbles over the eggs.
Arrange the cheese slices over the sausage, slightly overlapping the slices as needed. Place the top half of the rolls over the cheese.
Stir together the melted butter and Dijon mustard. Brush the mixture evenly over the tops of the rolls and sprinkle with everything bagel seasoning.
Bake uncovered for 10 to 12 minutes, until the cheese has melted and the tops are lightly golden brown.
Garnish with dried parsley, if desired. Rest for two to three minutes, then cut the rolls into 12 individual sliders and serve warm.