Melt the butter in a large skillet over medium heat. Add the onion, celery, carrots, and garlic. Cook until the vegetables are softened, about 5 minutes.
Add the flour and stir to coat the vegetables. Cook for 1 minute.
Pour the broth into a slow cooker and add the vegetables. Stir in the potatoes and corn.
Cover and cook on low for 6-8 hours or on high for 3-4 hours, until the vegetables are tender.
Stir in the milk, salt, and pepper. Simmer on low for 10 minutes.
Stir in the parsley and serve.
Interesting Facts
Corn chowder is a popular soup in the United States, especially in the American south.
It is usually made with a creamy base of milk or cream, and can be made with fresh or frozen corn.
Corn chowder is often served with crackers or croutons for added texture.