Heat a large Dutch oven or pot over medium heat. Add the oil and ham. Cook, stirring occasionally, until the ham pieces are golden brown, 8 to 10 minutes. Increase the heat to medium-high; add the onion, carrot, and celery, and continue to cook until the vegetables are slightly softened, about 5 minutes more. Add the garlic and cook 1 minute more.
Meanwhile, place the split peas in a colander. Rinse them well and pick through and discard any tiny pebbles or debris.
Add the peas, chicken stock, thyme, and bay leaf, if using. Bring to a simmer, then reduce the heat to medium-low and cook, uncovered, stirring occasionally, until the peas “split” open in the pot and are very tender, 1 hour and 30 minutes. (If the pot stops simmering during cooking, increase the heat to medium until it returns to a simmer, then reduce the heat back to medium-low). Add 1/2 to 1 cup of water to reach desired consistency.
Season with the salt and black pepper. Serve topped with parsley, if you like.
Excellent. If too salty cube a potato and add it during the last 10 minutes of cooking