Prepare the filling:In a large pan, heat the vegetable oil over medium heat. Add the chopped onion and cook for 2–3 minutes until soft and translucent. Stir in the minced garlic and grated ginger, cooking for another minute until fragrant.

Cook the beef:Add the ground beef to the pan, breaking it up with a wooden spoon as it browns. Cook until no longer pink. Drain off any excess fat if necessary.

Add the vegetables and sauces:Stir in the grated carrot and green onions, followed by soy sauce, oyster sauce, hoisin sauce, and sesame oil. Mix well to coat everything evenly.

Thicken the filling:Pour in the cornstarch-water mixture and stir until the sauce thickens and clings to the beef. Taste and adjust seasoning with salt and pepper. Remove from heat and let the filling cool completely before assembling the pies.

Preheat the oven:Set your oven to 190°C (375°F) and line a baking sheet with parchment paper.

Assemble the pies:Cut each sheet of puff pastry into squares or circles, depending on your preference. Spoon a generous amount of beef filling into the center of each piece. Fold over the pastry to form a half-moon or rectangle, then press the edges with a fork to seal.

Brush and top:Brush the tops of the pies with beaten egg for a glossy finish. Sprinkle sesame seeds on top if desired.

Bake to golden perfection:Bake in the preheated oven for 20–25 minutes, or until the pies are puffed and beautifully golden brown.

Serve hot:Let them rest for a few minutes before serving — the filling will be piping hot. Serve with sweet chili sauce or soy-vinegar dip for an authentic touch.