Rinse the peas in a sieve under cold running water and drain. Put the peas in a bowl and cover with hot water. Leave to stand for 20 minutes.
Heat 25g/1oz of the butter in a heavy-based frying pan and cook the onion, thyme and bay leaf very gently for 15 minutes, or until softened and only just beginning to colour. Stir regularly.
Drain the peas and add to the pan. Pour over 1 litre/1¾ pints water and bring to the boil. Reduce the heat slightly and simmer for 30-40 minutes, or until the peas soften and start falling apart. The liquid should be well reduced by this time.
Meanwhile, put the gammon in a large lidded saucepan and cover with cold water. Bring to the boil then discard the water (be careful as it will create a lot of steam). Cut the onion in half and stud each piece with cloves.
Take the peas off the heat, remove the bay leaf and blend with a hand blender until a thick purée. Beat in the remaining butter nutmeg and the egg. Season with salt and freshly ground black pepper.
Spoon the pea mixture into the centre of a piece of muslin. Tie the ends tightly with kitchen string just above the peas, allowing a little room for expansion.
Tuck the pease pudding and onion into the pan beside the gammon. Add the carrot, celery, bay leaves and peppercorns. Fill the pan with enough cold water to cover the gammon and return to the hob. Bring to a simmer, cover loosely with a lid and cook for 1-1¼ hours.
Remove the gammon and place on a board. Cover with foil and a couple of tea towels. Leave to stand for 10 minutes before carving. Ladle 300ml/10fl oz of the gammon stock into a heatproof jug.
For the mustard sauce, melt the butter in a heavy-based saucepan over a medium heat. Stir in the flour and cook for a few seconds before slowly adding the reserved stock, stirring well between each addition. Bring the sauce to a simmer, stir in the mustard and then the cream. Season, to taste, with salt and freshly ground black pepper.
Carve the gammon into thick slices. Unwrap the pease pudding and transfer to a warmed serving bowl. Serve a spoonful of pease pudding with a slice of gammon and drizzle over the sauce.