In a large soup pot or Dutch oven, combine the rinsed split peas, ham hock or ham bone, chopped onion, diced carrots, diced celery, minced garlic, chicken or vegetable broth, bay leaf, and dried thyme.
Bring the mixture to a boil over medium-high heat. Once boiling, reduce the heat to low, cover, and let it simmer gently for about 1.5 to 2 hours, stirring occasionally, until the peas are soft and the ham is falling off the bone.
Once the peas are cooked and the ham is tender, remove the ham hock or bone from the soup. Allow it to cool slightly, then shred the meat and discard any bones, fat, or skin. Return the shredded ham to the soup.
Taste the soup and season with salt and pepper as needed, depending on the saltiness of the ham.
If you prefer a smoother consistency, you can use an immersion blender to blend the soup until smooth. Alternatively, you can leave it chunky.
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