Sauté onion, carrot, and celery in butter in a large Dutch oven over low heat 10 minutes or until vegetables are tender.
Combine flour and cornstarch. Add to vegetables; cook over low heat, stirring constantly, until bubbly.
Combine broth and milk; gradually add to vegetable mixture. Cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Add cheese, soda, salt, and pepper, stirring until cheese melts. Stir in parsley. Ladle soup into individual bowls, and serve immediately.