Preheat oven to 400°F (200°C). Line a baking sheet with parchment paper.

Heat olive oil in a large skillet over medium-high heat. Add diced onion and sauté for 3-4 minutes until softened. Add minced garlic and cook 30 seconds until fragrant.

Add ground beef, salt, and pepper. Cook until browned, breaking the meat into crumbles, about 6-8 minutes.

Drain excess fat from the skillet. Stir in ketchup, mustard, and Worcestershire sauce. Cook for 2 more minutes, then remove from heat and let cool for 10 minutes.

Unfold the thawed puff pastry sheets on a lightly floured surface. Cut each sheet into 4 equal squares (8 squares total).

Spoon about 1/4 cup of the cooled beef mixture into the center of four pastry squares. Top with shredded cheddar cheese, leaving a 1/2-inch bare border around the edges.

Whisk egg and water to make an egg wash. Brush the bare edges with the egg wash. Place the remaining empty pastry squares on top.

Press edges firmly to seal, then crimp the edges tightly with a fork. Cut 2-3 small slits in the top of each pocket to vent steam.

Transfer pockets to the baking sheet. Brush the tops entirely with egg wash and sprinkle with dried parsley if desired.

Bake for 18-22 minutes until puffed, crisp, and deeply golden brown. Let cool for 5 minutes before serving.