Sauté the Aromatics: Heat the olive oil in a large, heavy-bottomed stockpot or Dutch oven over a medium heat. Add the chopped onions, carrots, and celery. Cook gently for 8-10 minutes, stirring occasionally, until the vegetables have softened and the onion is translucent but not browned. Add the minced garlic and cook for another minute until fragrant.

Combine the Ingredients: Add the rinsed split peas to the pot, along with the entire ham hock, the chicken stock, bay leaves, and dried thyme. Give everything a good stir to combine.

Bring to a Simmer: Increase the heat and bring the liquid to a boil. Once boiling, immediately reduce the heat to low, cover the pot with a lid, and let it simmer gently. A slow, gentle simmer is key here.

Simmer Slowly: Let the soup simmer for at least 90 minutes, or until the split peas are completely soft and have started to break down, and the meat on the ham hock is very tender. Stir the soup every 20 minutes or so to prevent the peas from sticking to the bottom of the pot.

Prepare the Ham: Carefully remove the ham hock from the pot and place it on a cutting board to cool slightly. Use two forks to shred the meat from the bone, discarding the skin, fat, and bone. Remove the bay leaves from the soup and discard them as well.

Finish the Soup: At this point, you have a choice. For a chunkier texture, simply return the shredded ham to the pot. For a smoother soup, use an immersion blender to pulse the soup a few times before adding the meat back in. I find that a few quick bursts creates a lovely creamy base while still leaving some texture. I used to struggle with getting this right until I discovered this technique.

Season and Serve: Stir the shredded ham back into the soup and let it warm through for a few minutes. Taste and season generously with freshly ground black pepper. You likely won't need much salt, as the ham hock is quite salty, but add a little if you think it needs it. Ladle into bowls, garnish with fresh parsley, and serve hot.