In a large skillet over medium heat, cook the breakfast sausage, breaking it up with a spatula, until fully browned and cooked through, about 6-8 minutes. If using onion, add it during the last 2 minutes of cooking. Drain any excess grease and set aside to cool slightly.

In a medium bowl, whisk together the 6 eggs, milk, salt, and pepper. In the same skillet (wiped clean or with a little oil), cook the eggs over medium-low heat, gently stirring, until softly set but still slightly moist, about 3-4 minutes. Remove from heat immediately—they will continue to cook from residual heat.

Preheat your oven to 400°F (200°C). Line a baking sheet with parchment paper. On a lightly floured surface, roll the thawed puff pastry sheet into a 10x14 inch rectangle. Cut it lengthwise into 4 equal strips (each about 2.5 inches wide).

Along the center of each pastry strip, layer: a portion of the cooked sausage, a line of scrambled eggs, and a sprinkle of shredded cheese, leaving about 1/2 inch at the top and bottom. Carefully roll each strip up from one long end to the other, enclosing the filling. Place seam-side down on the prepared baking sheet, spacing them about 2 inches apart.

Brush the tops of each roll-up lightly with the beaten egg wash. Sprinkle with sesame seeds if desired. Bake for 18-22 minutes, or until the pastry is puffed and deeply golden brown.

Let the roll-ups cool on the baking sheet for 5 minutes before transferring. Garnish with chopped fresh parsley. Serve warm on a white plate with blue accents for a beautiful presentation.