Place the split peas, onion, carrots, celery, garlic, and potato into the slow cooker.
Pour in the vegetable broth, then add the thyme and bay leaf.
Stir everything together to distribute the ingredients evenly.
Cover and cook on low for 7 hours or on high for 4 hours until the split peas are soft and the soup has thickened.
Remove the bay leaf, then season with salt and black pepper.
Ladle into bowls and top each serving with fresh parsley.