To make the pastry, sift the flour and salt into a mixing bowl and rub in the butter and lard or vegetable fat until the mixture resembles fine breadcrumbs. Add the beaten egg and water and mix to a firm dough. Wrap the dough in plastic wrap and chill for 30 minutes.
Preheat the oven to 220°C. Roll out just over half the dough into a round large enough to line the base and sides of a deep 20 cm pie plate. Line the plate with the dough, place a pie funnel in the centre and arrange the chicken around the funnel. Season to taste with the pepper and sprinkle with the parsley and onion. Arrange the ham on top and sprinkle with the mace and more black pepper.
Brush the edges of the dough with cold water. Roll out the remaining dough into a round large enough to cover the pie and place it in position, cutting a cross in the centre to accommodate the pie funnel. Press the edges of the dough together well to seal, then trim and decorate the edge with a fork or spoon. Decorate the top of the pie with leaves made from the trimmings, if desired.
Brush the pie all over with milk and bake in the centre of the oven for 15 minutes. Reduce the temperature to 190°C and continue cooking for 1 hour. If the pastry begins to brown too much, cover it loosely with foil.
Remove the pie from the oven. Put the cream into a saucepan, bring it almost to the boil and pour it carefully into the pie through the pie funnel. Serve as soon as the cream has been added.