Add the potatoes, ham, chicken stock, onion, celery, garlic, salt, and pepper to a large (at least 6 quart) slow cooker. Give everything a good stir, and then over and cook on LOW for 7-8 hours or HIGH for 4-5 hours.
In a small bowl whisk together the milk and cornstarch until combined and no lumps remain. Add the milk to the slow cooker and stir until combined. Cover the slow cooker and cook on HIGH for 20 minutes or until the chowder is thickened. Then, turn off the heat and stir in the cheese and sour cream until the cheese is melted and there are no streaks of sour cream.
Season to taste with salt and pepper and serve with extra shredded cheese.