1. Preheat the oven to 400°F (200°C) and line a baking sheet with parchment paper.

2. Cook the breakfast sausage links in a skillet over medium heat until browned and fully heated through, then transfer them to a plate to cool slightly.

3. In a bowl, whisk together the eggs, milk or cream, salt, and black pepper until well combined.

4. Lightly grease a nonstick skillet and pour in the egg mixture, cooking over medium-low heat while gently stirring until the eggs are just set and still soft, then remove from the heat to cool slightly.

5. Unfold the thawed puff pastry sheet on a lightly floured surface and gently roll it into a rectangle about 12×10 inches, then cut it into 8 equal rectangles.

6. Divide the scrambled eggs evenly along one long edge of each puff pastry rectangle, leaving a small border for sealing.

7. Sprinkle shredded cheddar cheese over the eggs on each rectangle, then place one sausage link on top of the cheese.

8. Roll the puff pastry tightly around the filling, tucking in the sides slightly as you roll, and place each roll seam-side down on the prepared baking sheet.

9. Brush the tops of the roll-ups with melted butter or beaten egg to help them turn golden and glossy as they bake.

10. Bake for 18–22 minutes, or until the puff pastry is puffed, deep golden brown, and crisp all over.

11. Let the roll-ups cool on the baking sheet for 5 minutes before serving, then garnish with chopped fresh chives or parsley if desired and enjoy warm.