Pre heat the oven to 86C. Place the gammon in an ovenproof saucepan with the onion, leek and carrot, then cover it with 1 litre of cold tap water.
Bring to a simmer over a medium heat, then cover the pan and place in the pre-heated oven for five hours.
Allow the ham to cool in the stock, then remove and strain the stock into a bowl, through a sieve lined with two layres of wet muslin.
Discard the vegetables and shred about 180g of the meat. Keep the rest chilled for use another time.
In the meantime, spread the peas on a baking tray lined with kitchen paper and allow to defrost completely (the paper absorbs the excess liquid that would otherwise dilute the pea flavour).
Melt 25g of the butter in a saucepan and add the shallot, garlic and bacon. Cook for five mins over a medium heat until soft but not coloured.
Add 750g of the ham stock bring to the boil and simmer for five minutes. Add all but 75g of the peas and the remaining butter and remove from the heat immediately.
Liquidise this mixture thoroughly in batches if necessary.
Strain through a fine sieve pressing through as many solids as poss and pour into a clean pan. Season with salt and freshly ground pepper.
When ready to serve, gently reheat the soup.
With a hand blender, aerate the soup until light and frothy, then add the ham and the remaining 75g of peas.