Prepare the Split Peas: Rinse the dried split peas thoroughly, removing any stones or debris. Set aside.
Sauté the Vegetables: Heat olive oil in a large soup pot over medium heat. Add the diced onion, carrots, and celery, and sauté until the vegetables are softened, about 5–7 minutes. Add the minced garlic and cook for another minute.
Add Ham and Broth: Stir in the diced ham (or ham hock) and let it cook for a couple of minutes. Add the vegetable or chicken broth, bay leaf, thyme, and split peas. Stir to combine.
Simmer the Soup: Bring the soup to a boil, then reduce the heat to low. Let it simmer for 1 hour to 1 hour 30 minutes, or until the peas are tender and the soup has thickened. Stir occasionally, and remove the ham hock once the meat is tender enough to shred.
Shred the Ham (if using ham hock): Once the ham hock is tender, remove it from the soup, shred the meat, and return it to the pot. Discard the bones and skin.
Final Adjustments: Taste and adjust the seasoning with salt and pepper. Remove the bay leaf before serving.
Serve: Ladle the soup into bowls and serve with crusty bread or crackers for the ultimate comfort meal.