In a large pot, add the rinsed split peas, ham bone (or diced ham), chopped onion, diced carrots, diced celery, minced garlic, and the broth.
Bring the mixture to a boil, then reduce the heat to a simmer.
Add the bay leaf and dried thyme. Cover and simmer for about 1 hour, or until the peas are soft and the soup has thickened.
If using a ham bone, remove it from the soup, cut off any ham, dice it, and return it to the soup.
Remove the bay leaf. For a smoother soup, you can use an immersion blender to puree the soup to your desired consistency.
Season with salt and pepper to taste.
Serve hot, garnished with chopped fresh parsley if desired.