Melt butter in a large pot over medium heat.
Sautée onions, celery, and garlic until fragrant and onions are tender.
Stir in potatoes, carrots, broth, salt, and pepper. Bring to a boil and reduce heat.
Cover, and simmer for 20 minutes.
Stir in salmon, evaporated milk, corn, and cheese. Cook until heated through or the fish is cooked.
Serve hot. Sprinkle freshly chopped parsley right before serving.