Put the split peas in a bowl with the bicarbonate of soda. Cover with cold water and leave to soak overnight.
Put the ham hock in a large saucepan, cover it with 1½-2 litres/2½-3½ pints cold water and bring to the boil. As soon as it has reached boiling point remove from the heat. Drain, wash the ham hock and the pan to get rid of any starchy foam.
Put the ham back in the pan and cover with water again. Add the whole onion studded with cloves, mace and bay leaves to the pan. Bring to the boil, then simmer for 1 hour.
Rinse the split peas and put in a saucepan, bring to the boil and boil for 10 minutes. Drain the peas and add to the ham hock pan along with the diced onion and carrot. Simmer until the peas are tender, this should take between 45 minutes to 1 hour. Top up with more water if needed.
Remove the ham hock, whole onion, bay and mace. Break up the ham hock, discarding the skin and bone and pull the meat into pieces.
Add the mustard to the soup and season with salt and pepper. Use a stick blender to blend to a rough purée, add the ham hock meat back into the soup and warm through.
Lightly whip the cream if using and fold gently into the soup. Serve with chunky bread.