Rinse the split peas under cold water and set aside.
Heat olive oil in a large pot over medium heat. Add the chopped onion and garlic, cooking until the onion is translucent.
Add the diced carrots, celery, and leeks. Cook for about 5 minutes until vegetables begin to soften.
Add the split peas, smoked ham hock (or diced bacon), bay leaf, and dried thyme to the pot. Stir to combine.
Pour in the water or chicken broth. Bring to a boil, then reduce heat to a simmer.
Cover and simmer for about 1 to 1.5 hours, stirring occasionally, until the peas are soft and the soup has thickened. If using, add the sauerkraut or chopped cabbage in the last 30 minutes of cooking.
Add the diced potatoes to the pot and continue to cook for another 20 minutes, or until the potatoes are tender.
Remove the ham hock from the pot. Shred the meat from the bone, discard any fat, and return the meat to the soup.
Season with salt and pepper to taste.
Enjoy your meal!