Peel the potatoes and cut into ¾”–1” cubes. Grate the cheese, cube the butter, and measure out seasonings.
Place the cubed potatoes and chicken broth, Italian seasoning, garlic powder, onion powder, ground sage, butter, and bay leaves on top in the slow cooker. Stir to combine.
Slow Cook (6–8 hours on LOW or 3–4 hours on HIGH) – Cover and cook until the potatoes are fork-tender.
In a small bowl, whisk the cornstarch into the cold heavy cream until smooth. Stir the mixture into the slow cooker and cook 30 minutes more, until thickened.
Take out the bay leaves and stir in the sharp cheddar cheese, cream cheese and balsamic vinegar until completely melted and smooth. Add salt and pepper to taste.
Spoon the soup into bowls, topped with shredded cheese, smoked chicken, sliced green onions