Heat 2 tablespoons of oil over medium-high heat in large Dutch oven or stockpot; add the hocks or joint to pot and brown on all sides.
Cover with eight cups of water and if desired, add a rib of celery, one carrot, an onion, and some black peppercorns to the pot. Bring to a boil, lower the heat to low and simmer for 2 hours to make the stock before moving on to making the soup.
For The Soup (Stovetop)
In a large soup pot, saute the onions over medium heat in olive oil until translucent (about 4-5 minutes) add the chopped garlic and cook another minute (being careful to not let it get too dark). Add the peas, ham & bone (or ham hocks/shank), carrots, and celery.
Tie the parsley and bay leaf together with kitchen string. Add the herb bundle, stock, paprika, and salt & pepper to taste. Bring to a boil over high heat. Lower the heat to a simmer; cover and cook (stirring often) 30 minutes.
Stir in the potatoes and cook until soup is thick and peas have almost disintegrated, about 30-40 minutes more.
Remove the pot from the heat, and remove the bone to a bowl to cool.
Pull meat from ham bone and shred.
Remove the herb bundle from the soup and discard.
Add the shredded ham and heat the soup to a simmer.
Taste and if needed, season with salt and pepper. If using, mix in a teaspoon of the vinegar. Taste, and add more vinegar as needed to brighten the flavors in the soup.
Serve hot.
Slow Cooker Instructions
Follow the instructions for the stovetop method up to step 2, where the garlic is added and cooked for a minute.
Transfer the sautéed vegetables and garlic to the slow cooker. Add the split peas, ham, bay leaf, thyme, and chicken stock to the slow cooker. Stir to combine.
Cover and cook on low for 8–9 hours or high for 4–5 hours, until the split peas are tender and the soup is thickened.
Remove the bay leaf and ham bone (if using). Shred any ham from the bone and return it to the soup. Season with salt and pepper to taste. If the soup is too thick, add water or stock to reach the desired consistency.
Serve warm, garnished with fresh herbs, if desired.
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Notes
If your bone isn’t meaty, or you don’t have a leftover ham to add to the soup, use thick sliced bacon or cubes of pancetta by browning it in the pan before and removing excess oil before cooking the onions.
Ham can be salty, so salt at the end to avoid over-salting.
Stir often as split peas can stick to the bottom of the pot as they cook.
Split peas absorb lots of liquid as they cook, so check the soup often and add extra stock as needed.
The peas in this soup only need to be cooked until tender, but if you like a smoother, creamier soup, cook them longer until they are soft and falling apart.
For an even silkier soup, puree it (before adding the shredded ham meat) with an immersion blender or in batches in a blender or food processor.
To make this recipe in the slow cooker, follow the instructions to where you lower the heat to a simmer and then add it to a slow cooker and cook on low for 4 hours, add the potatoes and then cook a further 1-2 hours.