Place the chicken in a large pan. Squeeze the onion with cloves and add it to the pan with the carrots, bay leaves, stock cube and peppers. Cover with cold water and bring to a boil, then reduce the heat and simmer until the chicken is cooked through. This will take around 45 minutes to 4/11 hours depending on the size of the chicken.
Meanwhile, make the dough. Sift the flour and salt together in a large bowl. Mince the cold butter and vegetable shortening and rub them into the flour until the mixture resembles fine crumbs. Mix just enough cold water to form a stiff dough. Turn this out onto a lightly floured surface and gently knead to form a smooth ball of dough. Wrap in cling film or place in a plastic bag and cool for at least 30 minutes.
When the chicken is cooked, remove the pan from the heat. Remove the chicken and place it on a plate. Return the pan to the heat and reduce the cooking liquid to about 250ml/9fl oz. Strain the reduced liquid into a pitcher and let it cool, then drain the fat and discard it.
When the chicken is cool enough to handle, cut the meat into pieces and discard the skin and bones.
For the sauce, remove the cloves from the onion. Place the onion in a food processor with the stock reserved. Mix until smooth, then add the milk and set aside.
Melt the butter in a pan and stir in the flour. Gradually add broth and milk, then bring to a boil, stirring continuously. Reduce the heat and simmer for 4-5 minutes to cook the flour flavor. Season, to taste, with salt and freshly ground black pepper, then fold the meat gently into the sauce. Reserve the mixture to cool.
Preheat oven to 220C/210C Fan/Gas 7. Roll two thirds of the dough and use it to line a 20-25cm/8-10in pie plate and add the cooled chicken mixture.
Pass the remaining dough to make a lid for the pie, brush the edge with beaten egg and press the edges together to seal.
Decorate the top of the pie with sheets made from pastry ornaments and brush everything with beaten egg. Punch a hole in the top of the pie to allow steam to escape, then bake in the preheated oven for about 45 minutes, or until the crust is golden brown.