Roll out the puff pastry and cut out 4 round sheets (10 cm diameter). Line 4 pie tins with the pastry sheets.
Heat butter in a pan over medium heat. Sauté the onion for 2-3 minutes until softened. Add the minced beef and fry for 3-4 minutes until browned. Stir in flour, Worcestershire sauce, water, salt and pepper. Bring to a boil, then simmer for 1-2 minutes. Remove from heat and let cool completely.
Pour the meat mixture into the 4 pie tins. Cut out 4 lids from the remaining puff pastry, place on top, and press down firmly. Pierce each lid in the center to allow steam to escape. Brush with beaten egg. Place the pie tins on a parchment-lined baking sheet. Bake at 190°C (374°F) for 20 minutes until the pastry is golden brown.