Toss the beef in the flour and brown in the oil in a large saucepan. Tie the bay leaf, thyme, and parsley to make a bouquet garni. Add the onions to the pan and toss about until they begin to soften, then add the carrot, celery, the bouquet garni, and seasoning.
Mash the anchovies and stir them in. Pour the Guinness over the top, stir well, cover, and cook very gently until the meat is almost tender, about 1 1/2 hours. (This can be done in the oven, if preferred.) Add the mushrooms and continue cooking for another 25 minutes. Allow the filling to cool.
Preheat the oven to 375˚F (190˚C).
Transfer the contents of the saucepan to a deep pie dish and check the seasoning. On a floured board, roll the pastry out into a large circle about 1 1/2 inches (4 cm) larger than the pie dish. Cut off the surplus 1 1/2 inches (4 cm) of pastry from around the edge of the circle in a long strip, and press this strip onto the dampened edge of the dish. Lay the remaining pastry circle (now the size of your dish) over the pie, pressing it onto the strip to attach it well and crimping the edges decoratively. Make a vent in the center and decorate the pie with leaves or flowers made from the pastry trimmings. Brush with the beaten egg and bake for about 35 minutes until the pastry is risen and golden.
Eat this with creamy mashed potatoes or boiled baby potatoes tossed in butter and parsley, or fresh crusty bread and a green salad.