Heat olive oil in a skillet over medium heat. Add the sliced onions along with a pinch of salt. Cook slowly while stirring occasionally until they turn golden brown, about 15-20 minutes. Set aside to cool.
In a mixing bowl, combine the ground sausage with the cooled caramelized onions, fresh thyme, and season with salt and pepper. Mix in optional cheese and mustard if desired.
Preheat your oven to 400°F (200°C) and prepare a baking sheet lined with parchment paper.
On a floured surface, roll out the thawed puff pastry sheets. Cut each sheet into rectangles measuring approximately 4×6 inches. Place a spoonful of filling on one half of each rectangle, fold over, and seal the edges.
Place each assembled roll onto the prepared baking sheet. Brush the tops with beaten egg and bake for 20-25 minutes until golden brown and puffed up.