Preheat the oven to 180C/365F/Gas 4.
For the pigeon, season the pigeon crowns well with salt and freshly ground black pepper, then rub each crown all over with the butter and mace and set aside for 30 minutes.
Heat a large ovenproof frying pan until hot, add the oil and sear the pigeon crowns on each side, until golden-brown all over, then place into the oven and roast for 12-15 minutes, or until cooked to your liking. Remove from the oven, remove from the pan and leave to rest in a warm place for five minutes.
For the sauce, pour out the excess fat from the pan, then add the shallots and fry over a medium heat for 2-3 minutes.
Add the sherry vinegar and white wine vinegar. Bring to the boil and reduce the liquid by half.
Add the stock and boil again to reduce the liquid by a third.
Add the butter and season, to taste, with salt and freshly ground black pepper.
Meanwhile, carefully cut the pigeon breasts away from the bone.
Strain the sauce into a clean pan and use half to baste the pigeon breasts.
Add the parsley and chervil to the remaining sauce in the pan and stir.
For the potato cake, increase the oven temperature to 200C/400F/Gas 6.
Place the potatoes into a bowl and add the clarified butter and season well with salt and freshly ground black pepper.
Heat four 15cm/6in diameter ovenproof frying pans and arrange the potato slices into the base of the pans, so that they cover the base of each pan, overlapping each other slightly. Repeat for three layers of potato discs in each pan, then transfer to the oven to cook for 10-15 minutes, or until the potatoes are golden-brown and cooked through. (You can use one larger pan to create a single, larger potato cake. NB: this may take longer to cook.)
For the peas, place the spring onions into a pan of boiling water and blanch for one minute. Drain the spring onions and refresh in iced water, then drain again.
Heat a frying pan, until just warm, then add the butter, peas and blanched spring onions. Cook for two minutes over a low heat.
To serve, carefully turn the potato cakes out into the centre of each of four plates. Place a spoonful of the peas and spring onions into the centre of each potato cake. Place three pigeon breasts on top of each pile of spring onions/peas and pour the remaining sauce over.