Rinse the split peas thoroughly under cold water and set aside. Chop the onion, carrots, and celery into small, even pieces. Mince the garlic.
In a skillet over medium heat, sauté the chopped onion, carrots, and celery with a splash of oil until they soften and the onions become translucent, about 5 minutes. This enhances their natural sweetness and aroma.
Transfer the sautéed vegetables to the slow cooker. Add the rinsed peas, minced garlic, dried thyme, bay leaf, and broth. Nestle the ham hock into the mixture if using. Season with a pinch of salt and pepper.
Cover the slow cooker with the lid and cook on low for 8 hours, allowing the peas to break down and the flavors to meld into a thick, velvety soup. Resist opening the lid during the first 4 hours to keep the heat steady.
Halfway through cooking, check the liquid level. If it looks too thick, stir in a little more broth to keep it creamy but not too watery.
Once the cooking time is complete, remove the ham hock. Shred the meat and discard any bones or excess fat. Return the shredded ham to the soup and stir well.
Taste the soup and adjust seasoning with more salt and pepper as needed. Remove and discard the bay leaf.
Serve the soup hot in bowls, garnished with fresh herbs if desired. The soup should be thick, creamy, and filled with hearty chunks of vegetables and tender ham.