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Heat a dutch oven or large, heavy-bottomed pot over medium heat. Add the olive oil. Once hot, add the onions, celery, carrots, salt, and pepper. Saute until the vegetables soften and lightly brown, about 8 to 10 minutes.
Add the thyme, bay leaf, and minced garlic. Saute for 30-seconds until fragrant.
Add the split peas and saute for 1 minute. Add the pork to the center of the pot. Add the water and chicken stock, stir, then bring to a boil.
Reduce the heat to medium-low, cover, and simmer. Stir occasionally so that the peas do not stick to the bottom of the pot, adjusting the heat as needed to maintain a gentle simmer. Flip the ham over 1 hour after cooking. Cook until the peas fall apart and lightly thicken the soup. The meat should pull off the bone and the vegetables are tender, about 2 hours.
Remove the bay leaf and discard. Transfer the ham to a cutting board. Remove the skin and discard. Pull the meat off the bone and dice it into small pieces.
For a smooth consistency, use an immersion blender to puree the soup. Alternatively, puree the soup in batches using a countertop blender. Leave a few cups of peas intact for a more rustic texture if desired.
Season the soup to taste with salt and pepper. Add the pork back to the soup and stir to combine.
Divide among bowls to serve and garnish with parsley.