Heat the oil in a large skillet over medium-high heat.
Add beef stew meat, and cook until browned on the outside.
Add the onion; cook and stir until tender, about 5 minutes. Stir in the mushroom gravy mix and 1 cup of water. Season with Worcestershire sauce, salt, and pepper. Turn heat to low, and simmer for 20 to 30 minutes.
Preheat the oven to 400 degrees F (200 degrees C).
Transfer the beef mixture to a casserole dish.
Roll out the puff pastry to cover the top of the casserole dish. Press edges onto the rim of the dish to seal.
Whisk together the egg and 1 tablespoon of water in a small cup using a fork.
Brush over the top of the pastry.
Bake for 20 minutes in the preheated oven, until the pastry is puffed and golden brown.