Peel and dice potatoes. Chop onion and celery. Mince garlic. Cube the softened cream cheese.
Add potatoes, onion, celery, garlic, broth, salt, pepper, and thyme to the slow cooker. Stir well.
Cover and cook on Low for 6 hours, until the potatoes are very tender.
Melt butter in a small saucepan over medium heat. Whisk in flour and cook 1 minute.
Ladle about 1 cup hot liquid from the cooker into the roux. Whisk until smooth.
Pour the mixture back into the slow cooker and stir to thicken.
Lightly mash some potatoes in the pot. Stir in cream cheese, heavy cream, and cheddar until melted.
Cook 10 minutes more on Low to warm through. Taste and adjust seasoning.
Ladle into bowls. Top with bacon, green onions, and extra cheddar if desired.