Rinse the dried split peas under cold water and remove any debris or stones. Drain and set aside.

In a large pot, heat some oil over medium heat. Add the chopped onion, carrots, celery, and garlic. Sauté until the vegetables are tender and slightly caramelized.

If using ham hock or bacon, add it to the pot and cook for a few minutes to release its flavors.

Add the rinsed split peas, vegetable or chicken broth, water, bay leaf, and dried thyme to the pot. Stir well to combine.

Bring the mixture to a boil, then reduce the heat to low and let it simmer uncovered for about 1 hour, or until the split peas are soft and cooked through. Stir occasionally to prevent sticking.

Once the split peas are cooked, remove the bay leaf and, if using ham hock, shred the meat and discard the bone.

Use an immersion blender or transfer a portion of the soup to a blender (in batches if needed) and blend until smooth. Be careful when blending hot liquids.

Return the blended soup to the pot and stir well to combine. If the soup is too thick, you can add more broth or water to achieve your desired consistency.

Season with salt and pepper to taste.

Serve the split pea soup hot and garnish with some chopped fresh herbs, croutons, or a dollop of sour cream if desired.