For the squab pigeons, singe off any remaining feathers or stubble by turning the pigeons over an open flame (use long heatproof tongs to do this). Chop off the neck bones and wings (trimming as close to the breast as possible) and reserve for making the sauce. Remove the wishbones to make carving easier.
Heat the clarified butter in a pan and sear the pigeons for 2-3 minutes on all sides, or until golden-brown all over. Set aside. You do not need to season the birds at this stage as the salt crust pastry will season the meat as it cooks.
For the salt pastry crust, combine the flour, salt, egg whites and water in an electric mixer fitted with a dough hook. Mix on a slow speed for 1-2 minutes, then scrape down the sides with a spatula. Turn the mixer back on and mix for 5-7 more minutes, or until the dough starts to come away from the sides of the bowl.
Knead lightly with your hands, then divide the dough into four equal pieces and wrap separately in cling film. Chill in the fridge for 20 minutes.
After 20 minutes, remove the dough from the fridge. On a floured work surface, roll each piece of dough to a thickness of 5mm and a diameter of about 28cm/11in. Using a small knife, cut out a circle from each piece of dough measuring 23cm/9in in diameter and set aside.
Gather all of the pastry trimmings and roll out to a sheet of 5mm thickness. Cut out eight pigeon wing-shaped pieces and set aside on parchment paper.
Roll up the pastry trimmings and divide into 4 equal pieces. Mould each piece into a round squab 'head', pinching one end to form a 'beak'. Press 2 cloves into each 'head' for eyes, then set aside on parchment paper.
Place a pigeon, breast-side down, into the middle of each circle of pastry and bring the edges up to wrap up the pigeon completely. Pinch the edges together to seal, making sure there are no gaps.
In a small bowl, beat together the egg yolks, milk and caster sugar for the eggwash. Brush the pastry 'wings' with some of the eggwash and attach 2 onto the sides of each wrapped pigeon. Brush the base of the pastry 'heads' and press firmly onto the wrapped pigeon.
Brush the completed pigeons all over with the remaining eggwash, except for the bases. Sprinkle rock salt over the breast, place the pigeons on a baking tray lined with foil and chill in the fridge until ready to bake.
For the sauce, melt the butter in a pan until foaming and gently fry the shallots for 2-3 minutes, or until softened but not coloured. Add the mushrooms during the last minute of cooking.
Meanwhile, heat the olive oil in a separate pan and sear the reserved pigeon necks and wings for 3-4 minutes, until golden-brown all over. Add the Madeira to the pan, scraping up any browned bits from the bottom of the pan to deglaze, then add the contents of the pan to the shallots and mushrooms and the brown chicken stock, bring to the boil and simmer for 10 minutes
Strain through a fine conical sieve, pressing down with a ladle to extract as much flavour as possible. Season, to taste, with salt and freshly ground black pepper. Reheat the sauce to order and serve in a gravy boat just before serving.
Preheat the oven to 220C/425F/Gas 7.
Bake the pigeons in the oven for 20-22 minutes (for medium; cook for 18 minutes for medium rare or 12 minutes for rare). Remove from the oven and set aside to rest for 5 minutes. The salt crust pastry is not just for visual effect, but also greatly enhances the taste and texture; the juices and flavour are sealed in and the slow build-up of heat keeps the flesh moist and tender.
For the garnish, bring a pan of water to the boil and place a steamer insert over the top. Add the cabbage to the steamer and steam for 2-3 minutes, or until just tender. Cut the cabbage into strips and place into a small serving bowl.
Heat the butter in a pan over a medium heat until foaming, then fry the shallots and garlic for 30 seconds. Increase the heat to high, then add the pied de mouton and cook for one minute. Add the white wine and cook for one minute, then add the girolles and cook for a further minute. Add the trompettes de la mort and herbs and stir well, then squeeze in the lemon juice and season, to taste, with salt and freshly ground black pepper. Spoon into a small serving bowl.
Present the baked pigeons, brushed with melted butter, on a large serving board with the bowls of cabbage and mushrooms on either side. To serve, first remove the pastry 'head', then slice open the salt crust to reveal the pigeon. Place a long fork inside the pigeon and lift it out onto the carving board, leaving behind the crust. Cut off the trussing string and serve the pigeon on a plate, allowing guests to help themselves to the sauce, cabbage and mushroom fricassee accompaniments.