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 the vegetable broth and add the butter and thyme sprigs.

Cover with the lid and cook on LOW for 6 to 8 hours or until the potatoes are very tender. You can also cook it on HIGH for 4 to 5 hours.

When done, remove the thyme sprigs and, if using, stir in the heavy cream.

Blend the soup with an immersion blender. If you only have a traditional blender, blend it in batches. Taste the soup for seasonings and adjust accordingly.

If the soup is too thick for your liking, add more vegetable broth to thin it out.

Ladle the potato leek soup into bowls, garnish with parsley and fresh thyme leaves, and serve.