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

In a mixing bowl, combine the diced onion, garlic, and mixed vegetables. Season with salt and pepper. Sauté in a pan over medium heat for about 5 minutes until softened.

On a floured surface, roll out the puff pastry sheets to about ¼ inch thick. Cut the sheets into rectangles, approximately 4x6 inches.

Place a spoonful of vegetable filling in the center of each pastry rectangle, followed by a sprinkle of shredded cheese. Be careful not to overfill.

Fold the pastry over the filling to create a pocket, pinching the edges to seal them well. Crimp the edges with a fork for extra security.

Brush the tops with the beaten egg for a shiny, golden finish.

Bake in the preheated oven for 18–20 minutes, or until golden brown and puffed up.

Let the rolls cool slightly before serving.