Instructions:
- Dice the onion and celery; mince the garlic. Peel and cube the potatoes into uniform bite-sized pieces (about 3/4 inch). Dice the ham.
- Place the diced potatoes, onion, celery, and ham into the basin of the slow cooker.
- Pour in the broth. Add dried thyme, bay leaves, and black pepper. Do not add salt yet.
- Cover the slow cooker. Cook on LOW for 6-8 hours or on HIGH for 3-4 hours, until the potatoes are fork-tender.
- About 30 minutes before serving, melt the butter in a small saucepan over medium heat. Whisk in the flour and cook for 1 minute until a blonde roux forms. Slowly whisk in the milk or half-and-half until smooth. Bring to a gentle simmer until slightly thickened.
- Remove the bay leaves from the slow cooker. Slowly ladle about 1 cup of the hot broth from the slow cooker into the milk/flour mixture while whisking constantly (tempering). Pour the tempered mixture back into the slow cooker.
- Stir everything well. Let the soup cook on HIGH for a final 15–20 minutes to allow the soup to reach your desired thickness. Taste and adjust seasoning, adding salt only if necessary.
- Ladle into bowls. Garnish immediately with shredded cheddar and fresh chives, if using.