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

2. Melt the butter in a skillet over medium low heat, add the sliced onions and salt, and cook for 20 to 25 minutes until soft, golden, and caramelized.

3. Stir in the garlic and thyme and cook for 1 minute more, then remove from the heat and let the onion mixture cool slightly.

4. In a large bowl, combine the sausage, caramelized onions, Gruyere cheese, Dijon mustard, and black pepper until evenly mixed.

5. Lightly flour a work surface and unfold the puff pastry sheets. Cut each sheet into 3 long rectangles for a total of 6 strips.

6. Divide the filling into 6 portions and shape each portion into a long log down the center of each pastry strip.

7. Fold the pastry over the filling and press the edges to seal, then place each roll seam side down on the prepared baking sheet.

8. Cut each long roll into 3 smaller pieces if serving as appetizers.

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

10. Lightly score the tops with a knife and chill the tray for 10 to 15 minutes.

11. Bake for 22 to 28 minutes until the pastry is puffed and deep golden and the filling is fully cooked.

12. Let the rolls cool for 5 minutes before serving warm.