Place chopped potatoes and leeks inside the slow cooker and set aside.

Heat olive oil in a skillet and add carrots and celery; cook for 4 minutes. Stir in garlic and cook for 20 seconds. Add the carrot mixture to the slow cooker. Stir in vegetable broth, butter, and thyme sprigs.

Cover with the lid and cook on LOW for 6 to 8 hours or until potatoes are tender.

Remove thyme sprigs and stir in heavy cream if using.

Blend the soup with an immersion blender until smooth. Adjust seasonings as needed.

If the soup is too thick, add more vegetable broth. Ladle into bowls, garnish with parsley, and serve.