For the filling, melt 60g/2oz of the butter in a large pan over a medium heat. Add the grated onions and stir over a low heat for 5-6 minutes.
Add the pigeons and cook for 10-12 minutes, turning occasionally.
Add salt and freshly ground black pepper, the parsley, coriander, the saffron in its water, the cinnamon and half the sugar and stir well.
Add the stock and bring to the boil. Reduce the heat to simmer, cover with a lid and cook over a low heat for 30 minutes, or until the pigeons are cooked and tender, stirring from time to time and adding water if necessary.
Remove the pigeons from the pan and allow to cool. Remove the pigeon meat from the bones and shred coarsely.
Meanwhile, heat the vegetable oil in a small pan, add the almonds and fry, stirring constantly until golden-brown. Remove the almonds with a slotted spoon and drain for a few minutes on kitchen paper. Crush the almonds coarsely in a mortar, or chop in a grinder for a very short time (they must remain coarse and not be ground to a paste).
Place the crushed almonds into a bowl with the remaining sugar and two tablespoons of the oil from the pan.
Return the pan in which the birds were cooked to the heat and simmer the cooking liquid for 10-15 minutes, stirring constantly, until the liquid has reduced to about 375ml/13fl oz.
Adjust the heat to very low and add the beaten eggs. Cook over the low heat, stirring all the time until the sauce thickens.
Preheat the oven to 180C/365F/Gas 4.
To assemble the pie, oil a 30cm/12in round baking tin. (Remember that once the filo pastry is out of the packet, you must keep it under a damp tea towel to prevent it from drying out.)
Layer five sheets of the filo pastry into the tin, brushing each one with melted butter and laying them at angles across each other, fanning them around the tin so that about 10cm/4in of each filo sheet hangs over the edge of the tin.
Then add two more sheets of filo across the base, buttering each sheet as you add it to the base. Trim any edges that are too big for the tin.
Cover the base with the egg mixture and then lay two more sheets of pastry over the egg mixture, trimming off any excess around the edges.
Spread the reserved shredded pigeon meat over the pastry, then top with another two layers of buttered filo pastry.
Sprinkle the almond mixture over the top and cover with the remaining sheets of filo, buttering each sheet before adding the next layer. Fold any excess pastry over the top to cover the pie, gently pushing the sheets down. When cooked, the sheets will curl upwards.
Brush the top of the pie with melted butter, then brush with beaten egg yolk.
Transfer to the oven and bake for 40 minutes, or until golden-brown and crisp.
To serve, turn out the pie onto a large dish. Sprinkle with icing sugar and cinnamon in a lattice pattern.