Place the diced potatoes, carrots, celery, onion, corn, peas, and garlic in the slow cooker.
Add the butter, thyme, salt, and pepper. Stir to coat the vegetables evenly.
Pour the vegetable broth over the mixture.
Cover and cook on low for 7 hours until the potatoes are soft.
Stir in the milk and heavy cream.
Cover again and cook on low for 30 more minutes to warm through and thicken slightly.