Prepare the pastry: In a large bowl, combine flour with butter and salt. Mix lightly with your fingertips until butter forms peasized pieces. Whisk together egg and 1 tablespoon of the water. Add to flour mixture all at once, mixing gently with your fingertips. You should be able to see chunks of fat, and the pastry should be moist enough to begin to stick together. If the pastry is too dry, add up to 2 more tablespoons of water.
Turn the pastry out onto a lightly floured work surface, dust with flour, and knead it until the pastry is smooth, about 3 to 4 times. Transfer to a plastic bag and form pastry into a disk. Refrigerate a minimum of 30 minutes, or as long as 3 days.
Meanwhile, heat 2 tablespoons of the oil in a casserole or Dutch oven. Add the steak and kidneys, season with salt and pepper, and cook, stirring, until just browned, about 3 minutes. Remove to a plate and reserve. Add 1 more tablespoon of oil to casserole, and add mushroom quarters. Cook over high heat, stirring, until light brown. Reserve on plate with meat. Add the remaining oil to the casserole, and add onions. Cook until well browned, about 5 minutes. Sprinkle the flour over the onions and stir so that the juices soak up the flour. Cook, stirring constantly, about 1 to 2 minutes.
Stir the Worcestershire sauce into the hot water, and pour over the hot onion mixture while whisking. Add the reserved meats and mushrooms, and any juices that have collected, and season with salt and pepper. Reduce the heat to low and simmer 3 to 4 minutes or until slightly thickened.
Preheat oven to 400 degrees F. Roll out the pastry to a thickness of 1/4inch. Fill a 9inch pie dish with the steak and kidney mixture. Dampen the edges of the dish with water, then fit the pastry on top, pressing it down well all around the edge to seal. Make a steam hole in the center, brush the top with milk and sprinkle with sea salt and freshly cracked black pepper. Bake for 25 minutes, or until pastry is golden.
c.1997, M.S. Milliken & S. Feniger, all rights reserved