1. Heat the olive oil in a large skillet over medium heat. Add the sliced onions and cook for 20 to 25 minutes, stirring often, until soft, golden, and caramelized.

2. Add the minced garlic and cook for 30 seconds. Add the ground sausage and cook until browned, breaking it up as it cooks.

3. Stir in the thyme, black pepper, salt, Worcestershire sauce, and Dijon mustard. Cook for 1 to 2 minutes more, then remove from the heat.

4. Let the filling cool slightly, then stir in the shredded Gruyere cheese and breadcrumbs.

5. Preheat the oven to 400°F and line a baking sheet with parchment paper.

6. On a lightly floured surface, cut each puff pastry sheet in half lengthwise to make 4 long rectangles.

7. Divide the filling into 4 portions and shape each portion into a log down the center of each pastry strip.

8. Fold the pastry over the filling, seal the edges, and place seam-side down. Cut each roll into smaller pieces.

9. Whisk together the egg and water, then brush the tops of the rolls with the egg wash.

10. Bake for 20 to 25 minutes until puffed and deeply golden. Rest for 5 minutes, garnish with parsley if desired, and serve warm.