Step 1: Caramelize the Onions

1. Heat a large skillet over medium heat. Add the butter and olive oil, allowing them to melt together.
2. Add the sliced onions, sugar, salt, and pepper. Cook, stirring occasionally, for 15–20 minutes, or until the onions are soft and golden brown.
3. Stir in the dried thyme and beef broth. Cook for an additional 2–3 minutes, allowing the liquid to reduce. Remove from heat and set aside.

Step 2: Prepare the Crescent Roll Dough

1. Preheat your oven to 375°F (190°C). Line a baking sheet with parchment paper.
2. Unroll the crescent roll dough and separate it into triangles along the perforated lines.

Step 3: Assemble the Roll-Ups

1. Place one slice of roast beef onto each triangle of crescent dough.
2. Add a spoonful of caramelized onions on top of the beef.
3. Sprinkle shredded cheese over the onions.
4. Roll up the crescent dough from the wide end to the point, encasing the filling. Place seam-side down on the prepared baking sheet.

Step 4: Add the Finishing Touches

1. Brush the tops of the roll-ups with beaten egg for a golden finish.
2. Sprinkle with dried parsley, if desired.

Step 5: Bake

1. Bake in the preheated oven for 12–15 minutes, or until the crescent dough is golden brown and cooked through.
2. Remove from the oven and let cool slightly before serving.