Start by making the pastry. Beat the butter and cream cheese in a mixer with the paddle attachment.
Separate one of the eggs, then add the yolk to the mixer and mix until thoroughly combined (save the egg white for another recipe).
In a separate bowl, stir together the flour and baking powder with 1 teaspoon of sea salt. Add it to the butter mix in a few stages, keeping it on a low speed until you have a smooth dough. Wrap it in clingfilm and chill in the fridge for about 30 minutes while you make the filling.
Peel and finely slice the garlic, onions and mushrooms. Pick and finely chop the parsley.
Put a lug of oil in a pan over a medium heat and fry the garlic and onions for 5 minutes, or until they start to colour. Add the mushrooms and fry for another 5 minutes.
Stir in the flour, then pour in the cream and 250ml of the chicken stock, and gently bring to the boil. Reduce the heat and simmer for a few minutes to thicken.
Stir in the chopped parsley, half the lemon juice and a good grating of nutmeg, season well, then shred and add the chicken. Set aside.
Pop the rice in a pan with the rest of the chicken stock and bring to the boil. Then cover with a lid, reduce it to a simmer and cook for around 15 minutes, or until the rice has absorbed all the stock. Remove from the heat and fluff a little with a fork.
Pick and finely chop the dill. Peel the hard-boiled eggs, chop them very finely, then mix them in a bowl with the dill. Set aside.
In the bottom of a 24cm pie dish, spread out a third of the rice, so it’s evenly covered. Layer on half of the chicken mixture, and top with half the egg mix. Repeat the process, finishing with the remaining rice.
Preheat the oven to 180ºC/gas 4.
On a floured surface, roll out the dough to the thickness of a £1 coin, so it will generously cover the pie. Place it on top and crimp the edges to seal. Cut a little cross into the top, making sure there’s a hole for steam to escape. Use any leftover pastry to make decorations for the top.
Beat the remaining egg together, then brush over the top and pop it in the oven for 25 to 30 minutes, or until the pastry is golden and the filling heated through.