To make the ham less salty: Put the ham hock in a large pan, cover with water and bring to the boil. Simmer for 5 minutes, drain and discard the water.
To cook the ham in an Instant Pot:
Put the stock vegetables and peppercorns in the Instant Pot (IP) inner. Place the ham hock on top then cover with cold or boiling water. Do not go past the Max line. Switch on the IP, lock on the lid and set the lever to 'sealing'.
Press the Manual button and, using the + or - button, change the time to 45 minutes. Leave until the time has elapsed and the indicator has counted down to zero. Switch off and leave until the pressure has naturally released.
Switch the lever to 'venting' then carefully remove the lid. Put the ham hock on a plate. Strain the stock, discarding the vegetables and peppercorns. Leave to cool then put in the fridge overnight.
To cook the ham on the stove:
Put the stock vegetables and peppercorns in a large saucepan along with the ham hock. Cover with cold or boiling water, put on a lid and bring to a simmer. Cook until the meat is very soft and almost falling off the bone (1.5 - 2.5 hours).
Remove the ham hock to a plate. Strain the stock, discarding the vegetables and peppercorns. Leave to cool then put in the fridge overnight.
Use two forks to shred the ham, discarding any fat or sinew. Put in a covered container in the fridge until needed.
Scrape any fat from the top of the cooled ham stock and discard it.
To make the soup in an Instant Pot:
Switch on the IP, put the olive oil and butter in the inner and press the saute button. When it's hot, add the onion, carrot, celery, leek and garlic. Saute until the vegetables are softening and browning (10-15 min).
Stir in the soaked, drained split peas, season with black pepper and saute for 2 minutes. Add 1 litre of the stock and stir. Press the Keep Warm/Cancel button.
Lock on the lid, making sure the lever points to 'sealing'. Press the Manual button and, using the + or - button, change the time to 25 minutes. Leave until the time has elapsed and the indicator has counted down to zero. Switch off and leave until the pressure has naturally released. Switch the lever to 'venting' then carefully remove the lid.
Check if the split peas are very soft and starting to fall apart. If not, cook for a further 5 minutes and repeat.
To make the soup on the stove:
Put the olive and butter in a large saucepan over a moderate heat. When they're hot, add the onion, carrot, celery, leek and garlic. Saute until the vegetables are starting to soften and brown (10-15 min).
Stir in the soaked, drained split peas, season with black pepper and saute for 2 minutes. Add 1 litre of the stock and stir. Put on a lid and bring to the boil. Take down to a simmer and cook gently until the split peas are very soft and starting to fall apart (35-50 min).
Using a stick blender, puree the soup until smooth. Add more stock for a thinner soup. Taste and season with more black pepper plus salt if needed.
Add most of the reserved, shredded ham and most of the chopped parsley. Gently reheat if necessary (press Saute on the Instant Pot if using).
Serve with a little of the remaining shredded ham and chopped parsley over each bowl (heat the ham in a microwave for a few seconds if liked).
If you don't have a ham hock, make the soup with approx 1.2 litres of low salt chicken or vegetable stock and 250 grams of chopped or shredded cooked ham. Go straight to Making the Soup, step 2