Prep. Heat olive oil and melt butter in a large pot or Dutch oven set over medium-high heat.

Saute. Add the chopped celery, carrots, and onions; cook for 4 minutes. Stir in garlic and cook for 1 minute.

Add liquids, peas, and herbs. Stir in the chicken broth and water. Stir in the split peas, bay leaves, thyme, and oregano; season with salt and pepper. Don’t use too much salt because the ham hocks are already salty.

Add ham and cook. Add the ham hocks to the pot and bring the mixture to a boil. Reduce heat to low, cover the pot, and let simmer for about 1 hour and 15 minutes, stirring occasionally. The soup is ready when the peas are soft. Start checking it for doneness around the 55-minute mark.

Shred the meat. Remove the ham hocks from the soup and let rest for several minutes, or until cooled enough to handle. Then, shred or chop up the meat into smaller pieces. Discard the bones and skin.

Finish and serve. Add the chopped ham back into the soup and cook for 1 minute. Remove from heat. Taste the soup for salt and pepper and adjust accordingly. Ladle the split pea soup into bowls, garnish with parsley, and serve.