Chicken and mushroom must be one of the favourite UK savoury pie fillings. The creamy sauce enveloping the tender chicken and mushroom chunks, all encased in crispy pastry is just wonderful.
Stir the salt into the flour in a large bowl. Pour over half of the fat/water and stir it in until the water has been incorporated. Do the same with the other half of the water. Tip the dough out onto a worktop and knead it by hand to get any final bits of flour mixed in. Wrap it in plastic film and leave to cool. It needs to be about room temperature by the time you use it.
Peel the onion and chop into small pieces. Heat some oil on low in a frying pan. Add the onions and cook until softened - do not brown them. Add the onion to the sauce. Wash the mushrooms and cut them into small pieces. Heat some more oil in the frying pan and cook the mushrooms until they just start to release moisture, then add them to the sauce. Chop the chicken breasts into small chunks, a bit over a centimetre (half an inch). Add the chicken to the sauce, stir well, and cook for about 5 minutes. Remove from the heat and let it cool down. Stir in the cream and place the filling in the fridge to cool completely.
Spoon the filling into the case, saving a bit of the sauce to use as gravy when you serve it. Moisten the rim with cold water, and place the lid on. Press it down all around with your thumbs, then lift up the edge of the pie, work it between your fingers to get it nice and smooth, and crimp it any way you like. Make some holes in the top with a fork, paint the top and the crimp with beaten egg, and sprinkle some random bits of oregano around the edge for decoration. You could also decorate it with thinly-sliced, sauteed mushrooms.
Place in the oven and bake for about 40 minutes, but check it after 30 minutes just to be sure it's not overbaking.