Potato Ham Chowder

Name: Potato Ham Chowder
Ingredients: 2 tablespoons butter (divided); 3 slices bacon (chopped); 2 cups chopped ham; 1 medium yellow onion (chopped); 3 garlic cloves (minced); 1 teaspoon Italian seasoning; 1/2 teaspoon dried oregano; 1/2 teaspoon fresh thyme; 3 potatoes (chopped (see note)); 15 oz can whole kernel corn (drained and rinsed); 1 teaspoon salt; 1/4 teaspoon black pepper; 1 cup 2% milk; 4 cups vegetable stock; 1 cup half and half; 1 tablespoon cornstarch; 1 cup shredded cheddar cheese